Rangers pull level with Celtic after 3-1 win at Hamilton
Steven Gerrard's men took an early lead through Ryan Jack but were quickly pegged back as impressive Hamilton youngster Lewis Smith squared things up.
But Kent, who spent last season on loan at the Scottish giants, restored the visitors' lead just before half-time, before wrapping things up in stoppage time.
Rangers dominated the opening 45 minutes but eased off after the break and were lucky not to drop points as Hamilton threatened an equaliser.
The win means Rangers join title rivals Celtic on 34 points, with the reigning champions remaining top on goal difference.
"At times we have to go and get the second goal quicker," Rangers boss Steven Gerrard told BT Sport.
"We were poor for Hamilton's goal, we were poor on three or four occasions throughout the game where we haven't won the first header and we haven't been in the right position to cover."
With Rangers top-scorer Alfredo Morelos only touching down back in Glasgow 24 hours before kick-off following international duty with Colombia, Gerrard decided to start with him on the bench.
The visitors opened the scoring when James Tavernier skipped past Scott Martin down the right before firing in a low cross. Centre-back Jamie Hamilton stopped the cross but succeeded only in setting the ball on a plate for Jack to roll home his fourth goal of the season.
But the smile was soon wiped off Gerrard's face as Accies levelled in the 14th minute,19-year-old Smith heading in after his initial effort had been blocked.
Hamilton kept Rangers at bay but their luck ran out two minutes before the break as Kent produced a moment of quality to put Rangers back in front, rifling an unstoppable strike into the top corner.
Morelos was introduced with seven minutes left but that was enough time to see him grab an assist three minutes into stoppage time as he rolled the ball to Kent, who calmed the fraying nerves of the away fans with a cool finish.