The visitors were reduced to 10 men after 25 minutes when Ryan Tafazolli was sent off for a lunging challenge on Andrew Shinnie and Town made them pay.
Top scorer Collins, who had opened the scoring after eight minutes, added a second before half-time and completed his hat-trick eight minutes after the break.
Luke Berry then rounded off the scoring to give Luton a first win under interim boss Mick Harford.
Pompey’s defeat to Oxford at the Kassam Stadium saw Luton close the gap at the top.
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It also took the home side out of the relegation zone.
Substitute winger Adam Hammill marked his Scunthorpe debut with a stunning late goal as his side came from behind to draw 1-1 with third-placed Sunderland.
The Black Cats had looked on course for all three points thanks to Josh Maja’s 16th goal of the season just before the hour mark, but winger Hammill curled the ball into the top corner from the edge of the box with three minutes to go.
Kieffer Moore spearheaded Barnsley to a 4-1 victory over bottom club AFC Wimbledon as the Tykes extended their unbeaten league run to seven games.
Moore’s 15th goal of the season and one from Mamadou Thiam earned the visitors all three points after Joe Pigott had cancelled out Cauley Woodrow's opener. Cameron McGeehan then added some late gloss with the Reds’ fourth.
Stephen Humphrys netted a brace on his debut as Southend thrashed lowly Bradford 4-0 at Valley Parade to record their sixth away win of the season.
United led 2-0 at half-time thanks to goals from Simon Cox and Sam Mantom and Humphrys struck twice after the break to complete the rout.
Andy Cook scored his first EFL hat-trick as Walsall ended a run of six games without a win by beating Gillingham 3-0 at Priestfield.
Plymouth's Portuguese striker Ruben Lameiras scored twice as his side came back from 1-0 down – following former Pompey striker Conor Chaplin’s opener – to beat Coventry 2-1 and make it three league wins in a row.
Fleetwood held on for a point after a second-half onslaught from Rochdale in a 1-1 draw at the Crown Oil Arena.
The visitors led 1-0 thanks to Paddy Madden's goal but were reduced to 10 men early in the half when Louie Coyle was sent off for a two-footed challenge on Joe Rafferty.
Dale forced the visitors back inside their own penalty area for long periods and eventually equalised through Ian Henderson to end their four-match losing run.
Centre-back John Brayford completed his brace with a headed a last-minute equaliser as Burton Albion denied Doncaster at the Keepmoat.
It had looked set to be a senior EFL debut to remember for Tyler Smith as he came off the bench to score twice to overturn an early opener from Brayford as it finished 2-2.
Centre-back Sido Jombati headed a 57th-minute winner as Wycombe pushed Bristol Rovers into the relegation zone with a 1-0 win at the Memorial Stadium, while a dramatic stoppage-time penalty from Karlan Grant secured Charlton a last-gasp 1-0 victory over Accrington Stanley at The Valley.
Both sides were a man down after Accrington goalkeeper Jonny Maxted and Charlton striker Lyle Taylor were dismissed eight minutes from time following a mass brawl in the penalty box.
Elsewhere it finished 0-0 at Bloomfield Road between Blackpool and Shrewsbury Town.