Matt Godden scored twice but it wasn't simple for Posh.
They fought back to beat 10-man Bromley and move into the second round of the competition.
Godden scored either side of the break to send the League One high-flyers through and ultimately end their National League opponents' hopes of an unlikely scalp.
But the turning point in the match came as Bromley's Frankie Raymond was sent off for an altercation with Peterborough's George Cooper when the home side led 1-0.
They had taken the lead five minutes before half-time when former Pompey loanee Frankie Sutherland's free-kick was met by veteran centre-back Roger Johnson, who leapt highest to nod in over Aaron Chapman.
It was seconds before the break when the Ravens were reduced to 10 men as Raymond needlessly tussled with Cooper and was dismissed for violent conduct.
The resulting free-kick led to Peterborough's equaliser as Godden curled home a beautiful strike past David Gregory to turn the tide for the EFL side.
Posh took the lead in the 56th minute when Jason Naismith's cross was met brilliantly by Godden who fired his shot first time into the bottom corner.
The visitors were comfortable for most of the second half and killed the game off in the 84th minute when Joe Ward beat the offside trap to coolly slotted beyond Gregory.
Conor Chaplin came on as a substitute for Coventry but could not rescue them from a 3-2 exit away to Walsall.
The match was marred by a pitch invasion and bottle-throwing incident.
Referee Thomas Bramall threatened to abandon the game after Coventry fans invaded the pitch and a bottle was thrown following Luke Thomas' superb equaliser for the Sky Blues.
City had deservedly fought back from 2-0 down but Nicky Devlin collected Liam Kinsella's through-ball to lash Walsall's 77th-minute winner into the top corner.
The Saddlers first led on 12 minutes as Zeli Ismail's inventive backheel found Andy Cook six yards out and he turned to poke past City keeper Lee Burge.
Walsall doubled their lead on 28 minutes as Josh Ginnelly pounced on Jordan Thompson's under-hit backpass to prod beyond Burge.
City pulled one back five minutes later as Jonson Clarke-Harris blocked Jon Guthrie's clearance and raced clear to slot home.
Thomas' excellent 20-yard volley crept under Roberts to make it 2-2 on 56 minutes but Walsall rallied and Cook's looping header hit the bar before Devlin's winner.
Chaplin was sent off after Walsall netted the decisive third but the former Pompey striker couldn't salvage anything for Coventry.
Other League One high-fliers to progress were Barnsley who thrashed Notts County 4-0 and Luton who beat Wycombe 2-0.
The Emirates FA Cup second round draw will take place from 7pm on Monday.
The draw will be held at The Beveree, home of National League South side Hampton & Richmond Borough, ahead of their first round tie against Oldham Athletic, and will be broadcast live on BBC Two.