Going ahead early-on through Ryan Jack, Gers were pegged-back by Lewis Smith before Kent scored at both the end of the first and second halves to ensure the three points go back up the M74 to Ibrox.
From the side which faced Livingston just before the international break, boss Steven Gerrard made just the one change with Jermain Defoe replacing Alfredo Morelos.
After dominating the opening few minutes in terms of possession, Gers first opportunity arrived on seven minutes – and it was taken superbly by Jack for his fourth goal of the season.
After working the ball well down the right, James Tavernier did superbly to get away from Scott McMann before crossing into the six-yard box.
Jamie Hamilton cleared the ball, but it went only as far as Jack, who hit it first time and curled the ball expertly beyond Luke Southwood from around 12-yards out.
It was just the start the visitors were looking for, and they very nearly had a second four minutes later. Picking the ball up just inside the Accies’ half, Ryan Kent drove for goal and just kept going and going before letting fly 20-yards out and seeing his effort come off the right-hand post.
Southwood then denied Jermain Defoe at close-range when Joe Aribo fed the striker with an excellent ball before on 13 minutes, with their first attack, Accies levelled.
Marios Ogkmpoe dug out a cross to Steve Davies at the back post, and he did superbly to keep the ball alive before getting it back across goal to Lewis Smith to loop a header beyond Allan McGregor.
Jack came close to a second with a decent effort from 25-yards which Southwood did well to hold onto, before Southwood made an even better stop from the midfielder, pushing an effort from similar distance round the post with one hand.
Connor Goldson had a headed effort on the end of a Borna Barisic corner held by the goalkeeper, while Jack had a third effort on goal from that distance, this time his powerful effort going just over the bar.
Jack was absolutely running the show, and he picked out Tavernier with an exquisite ball in-behind the defence, but after taking a touch in order to get his shot away, Southwood bravely dived in to claim the ball at the feet of the skipper.
The goal was certainly coming, and finally, on 43 minutes, it arrived thanks to a howitzer of a strike from Ryan Kent – his first goal since signing permanently for the club at the end of the summer window.
Shifting the ball onto his left foot 25-yards from goal, slightly to the right of the target, he unleashed a wicked drive which whizzed into the top-left corner, well beyond the reach of Southwood.
Filip Helander headed another Barisic corner over in the one minute of injury time at the end of the half, but 2-1 is how things remained as the teams headed down the tunnel.
The legs of Southwood denied Aribo in the opening minutes of the second half, while Accies threated again through Ogkmpoe.
A Barisic free-kick went loose in the box and almost ran for Goldson to turn home, while Accies missed a sitter on 64 minutes, with George Oakley’s ball across the face of goal somehow being sent wide by Mickel Miller from two-yards out.
Helander missed a great chance at the other end on 76 minutes to put the game to bed, rising well to head a Kent free-kick wide of target under little pressure.
McGregor had to be lively to grab an Oakley header out of the air as Accies pushed for the equaliser in the final 10 minutes, but as they committed men forward, Gers went on to punish them in the third minute of stoppage time.
A super Alfredo Morelos knock-down for Ryan Kent on the edge of the area allowed the winger to sweep a super finish into the bottom-left corner to secure the three points and make it six wins on the spin for the Light Blues in all competitions.
RANGERS: McGregor; Tavernier, Goldson, Helander, Barisic; Kamara, Jack, Aribo (Davis, 77); Kent, Defoe (Morelos, 83), Arfield (Ojo, 68).
SUBS: Foderingham, Flanagan, Katic, Stewart.
HAMILTON ACADEMICAL: Southwood, McGowan, McMann, Hunt, Davies, Miller, Goic, Easton, Smith (Cunningham, 80), Hamilton, Ogkmpoe (Oakley, 55).
SUBS: Fon Williams, Collar, Mackinnon, Moyo, Want.
REFEREE: Steven McLean
ATTENDANCE: 5100