Paul Doswell’s men are aiming to spring a massive FA Cup shock at a Charlton Athletic side who sit three tiers and 65 places above them in the pyramid.
Hawks are aiming for their first ever away win against a side in the top three tiers, while Charlton have never lost at home to a non-league club in the FA Cup since being elected to the Football League in 1921.
This Saturday’s trip to The Valley is the first time since 2014 that Hawks have faced EFL opposition in the world’s greatest club knockout competition. On that occasion, they were beaten 3-0 at home in the first round by Preston North End.
Prior to that, the club had faced Millwall, Notts County, Swansea City, Liverpool and Brentford in FA Cup action - three of those coming in the never-to-be-forgotten run to the fourth round in 2007/08.
Here, The News looks back at Hawks’ previous games against Premier League/EFL opposition.
Hawks 1 Millwall 2
1st rd, 2006/07
In a game switched to Fratton Park on police advice, Hawks were narrowly beaten by the club who had reached the FA Cup final three seasons earlier.
Ben May gave the three tiers higher Lions a fifth minute lead in front of a Monday night crowd of 5,793, with Rocky Baptiste levelling 11 minutes after the restart.
Adam Dunne’s 71st minute 20-yarder proved the difference in Hawks’ first ever meeting with a Football League club.
Just seconds earlier, Lions keeper Lenny Pidgeley had produced a stunning save to keep out a Richard Pacquette header.
Hawks: Shane Gore, Michael Warner, Justin Gregory (Dean Holdsworth, 73), Tony Taggart, Tom Jordan, Luke Byles, Mo Harkin (Craig Watkins, 83), Jamie Collins (Fitzroy Simpson, 83), Richard Pacquette, Rocky Baptiste, Brett Poate.
Notts County 0 Hawks 1
2nd rd, 2007/08
Having beaten one division higher York City away in the first round, Hawks stunned two tiers higher Notts County at Meadow Lane to reach the third round proper for the first - and so far only - time in their history.
There were only three minutes remaining when sub Tony Taggart sent the 261 travelling fans into ecstasy with a shot that seemingly took an age to roll past Magpies keeper Kevin Pilkington and into the net.
Taggart had been introduced four minutes after the restart in place of the injured Richard Pacquette.
Hawks: Kevin Scriven, Justin Gregory, Brett Poate, Charlie Oatway (Shaun Wilkinson, 46), Jay Smith, Neil Sharp, Mo Harkin, Jamie Collins, Richard Pacquette (Tony Taggart, 49), Rocky Baptiste, Alfie Potter.
Swansea City 1 Hawks 1
3rd rd, 2007/08
For the second round running, Hawks dramatically struck in the 87th minute - this time to earn a replay against League 1 leaders Swansea City.
With both sides down to 10 men, Tony Taggart - again on as a sub - lofted in a cross for Rocky Baptiste to net at the far post.
Shaun Gale’s side had fallen behind in the 74th minute when Andy Robinson curled a free-kick past Kevin Scriven’s reach.
Brett Poate was sent off following a two-footed challenge and Swansea captain Alan Tate was also dismissed for his part in the aftermath.
Hawks: Kevin Scriven, Justin Gregory, Brett Poate, Charlie Oatway (Wilkinson, 54), Jay Smith, Phil Warner, Mo Harkin (Tony Taggart, 83), Jamie Collins, Richard Pacquette (Slabber, 83), Rocky Baptiste, Alfie Potter.
Hawks 4 Swansea City 2
3rd rd replay, 2007/08
Quite simply, the most memorable night in the history of Havant & Waterlooville Football Club.
An astonishing result - against a side 83 places higher in the pyramid - catapulted Hawks into the eye of a worldwide media storm.
Not only had Shaun Gale’s National League South part-timers knocked out Roberto Martinez’s League 1 leaders, but in doing so they had booked a fairytale fourth round trip to Anfield.
Hawks took an early lead when Brett Poate swung in a cross and Swans defender Garry Monk headed into his own net.
The hosts led 2-0 on 25 minutes, Jamie Collins bundling in an effort, and Hawks were in dreamland 12 minutes later when Rocky Baptiste was left with a simple tap-in.
Swansea hit back immediately through Guillem Bauza and could have had a second before half-time, but Kevin Scriven saved Leon Britton’s spot-kick.
Jason Scotland sent Hawks nerves jangling a few minutes after the restart, but midway through the half Tom Jordan's header sealed a famous victory. Thirteen years on, it remains the club’s greatest cup success.
Hawks: Kevin Scriven, Justin Gregory, Brett Poate, Charlie Oatway (Wilkinson, 43), Jay Smith (Jordan, 46), Phil Warner, Mo Harkin, Jamie Collins, Richard Pacquette (Slabber, 78), Rocky Baptiste, Alfie Potter.
Liverpool 5 Hawks 2
4th rd, 2007/08
For 32 minutes in the first half at one of the world’s great sporting cathedrals, the part-timers led the millionaires in their own playground.
Incredibly, Hawks - 122 places and five divisions lower in the football pyramid - took an eighth minute lead against Liverpool through Richard Pacquette. They held it until the 27th minute, before Leiva Lucas equalised.
Even more incredibly, Hawks were back in front four minutes later - silencing the home fans again thanks to a strike from loanee Alfie Potter.
Liverpool didn’t level until the 44th minute, Yossi Benayoun scoring the first of what would prove to be a hat-trick.
Peter Crouch added a fifth goal in the closing stages as Hawks did themselves proud in front of a crowd of 42,566 on the biggest day of their lives.
Hawks: Kevin Scriven, Jay Smith, Phil Warner (Tony Taggart, 40), Shaun Wilkinson (Charlie Oatway, 74), Tom Jordan, Neil Sharp, Mo Harkin, Jamie Collins, Richard Pacquette (Jamie Slabber, 57), Rocky Baptiste, Alfie Potter.
Hawks 1 Brentford 3
1st rd, 2008/09
Hawks couldn’t repeat their previous season’s cup heroics, losing to a Brentford side who ended the season as League 2 champions.
Marvyn Williams gave the two tiers higher Bees a 40th minute lead after Kevin Scriven blocked Nathan Elder’s shot in front of a crowd of 1,631 and a live ITV nationwide audience.
Charlie MacDonald double the advantage after the restart, but Ian Simpemba’s 73rd minute bullet header gave the Hawks hope.
That was snuffed out eight minutes from time when Elder stretched to convert MacDonald’s cross.
Hawks: Kevin Scriven, Jay Conroy, Jay Gasson, Jamie Collins, Gary Elphick, Ian Simpemba, Matt Gray (Charlie Henry, 55), Gary Holloway, Luke Nightingale (Paul Booth, 80), Craig Watkins, Shaun Wilkinson (Brett Poate, 69)
Hawks 0 Preston North End 3
1st rd, 2014/15
Aston Villa loanee Callum Robinson fired a hat-trick as Preston avoided an FA Cup banana skin against a Hawks side that ended with just nine men.
Robinson scored twice inside the first half-hour for the three divisions higher visitors and completed his treble with an 81st minute penalty after Warren Cummings had been dismissed for handling on the goalline.
Hawks were already down to 10 men at the time having had Brian Stock sent off just before the hour mark for two bookable offences.
Hawks: Ryan Young, Dan Strugnell, Warren Cummings, Brian Stock, Brian Dutton, Ed Harris, Ben Swallow (Perry Ryan, 62), Scott Donnelly, JJ Hooper (Alan Connell, 72), Bradley Bubb (Shamir Mullings, 62), Josh Huggins.