Pelly-Ruddock Mpanzu opened the scoring in the 56th minute with an outstanding curling effort and six minutes later Harry Cornick scored his fourth goal of the season.
In the 95th minute, the Robins' centre-half Ashley Williams diverted the ball into his own net, which sealed all three points as Town moved up into 16th place in the Championship.
The first 20 minutes set the tone for an enthralling encounter, an open game which Luton took control of after a few Bristol City chances.
The Robins had two opportunities in the space of two minutes, both of which fell to Tommy Rowe.
First the left-wing-back forced James Shea into a good save from distance and then moments later tried to go around the keeper, before chipping over the bar from a tight angle.
Town were next to venture forward and went very close to scoring the first goal. Izzy Brown did well to carry the ball through midfield and find Dan Potts available in plenty of space on the left.
The left-back then crossed the ball, which Collins tried to direct goal-wards, but it was deflected just wide of the post and behind for a corner.
Pressure from the Hatters didn’t end there. Matty Pearson carried the ball forward and found Brown with space in-behind, the midfielder then passed to Ryan Tunnicliffe, but his effort was gathered by Bentley.
Luton’s best chance of the half came just before the 30 minute mark as Mpanzu set the ball for Brown, who from the edge of the box, produced a fierce shot which Bentley tipped onto the post.
Mpanzu then went close himself just before half-time but his low drive from the edge of the box was parried behind for a corner.
The second half started with much the same intensity, but Luton’s pressure finally paid off as Mpanzu opened the scoring in the 56th minute.
After winning possession back from the Robins, Town moved forward swiftly and ball found its way out wide on the left to the midfielder, who cut in and unleashed a brilliant, curling effort straight into the top corner.
The 26-year-old’s cracker was his first goal in the Championship, meaning he has now scored for Luton in four different divisions since arriving in the Conference title-winning season from West Ham.
In the 62nd minute, the home crowd were on their feet again as Harry Cornick doubled Town’s lead. Brown played a perfectly timed ball in-behind for the forward to run onto and Cornick produced a calm finish to score his fourth goal of the campaign.
Bristol City were pushing to get back into the game but James Shea – who made his first league appearance of the season – was on hand to keep the clean sheet intact.
It was two Robins substitutes – Niclas Eliasson and Rodri – who linked up, but the latter’s glancing header was saved well down low by Shea, who tipped the ball onto the post.
With just over 15 minutes to go, Luton quickly scurried forward trying to seal all three points, which Collins came agonisingly close to doing.
Cornick switched the ball across the pitch and found Brown, who knocked the ball forward to Collins but the onrushing Bentley saved one-on-one.
Adding to the visitor’s despair and the home crowd’s jubilation, Rodri was denied a debut goal as his effort was ruled out for offside in the dying embers.
With the last attack of the game, Luton scored their third as Tunnicliffe’s cross was put into the back of the net by Ashley Williams, rounding off a superb day for the Hatters which marks their biggest Championship victory to date.
TOWN: Shea, Bree (Bolton 45), Bradley (C), Pearson, Potts, Cranie, Tunnicliffe, Mpanzu, Brown (McManaman 76), Cornick (LuaLua 88), Collins. Subs not used: Shinnie, Sluga, Jones, Butterfield.
Yellows: Tunnicliffe, Mpanzu
Goals: Mpanzu, (56) Cornick (62), Williams OG (90+4)
BRISTOL CITY:Bentley, Hunt, Baker, Williams, Moore (Eliasson 58), Rowe, Brownhill (C), Massengo, Palmer (O’Dowda 58), Diedhiou (Rodri 64), Weimann. Subs not used: Wright, Semenyo, Pereira, Maenpaa
Yellows: Diedhiou, Hunt
Referee: Graham Scott
Attendance:10,064 (1,032 away)
