John Lundstram’s red card in the first half pitted Steven Gerrard’s side in a tense first-leg encounter, but Alfredo Morelos struck after the break to claim the victory.
The Premiership champions now take a slim lead over Armenia next week, knowing that avoiding defeat will once again secure a move to the group stage.
Here’s how they rated Thursday night.
ALLAN McGREGOR : Recorded his 90th European appearance for Rangers and had little to do other than step out of his box for a quick release – 6
JAMES TAVERNIER : I’m still not playing with the verve and vigor that embodied last season. Nothing wrong with his desire and his help for Morelos was great – 6
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CONNOR GOLDSON : Thrown a few dangerous diagonals at Kent early on and must have been defensive alert on occasion when Alashkert busted out and got some heads off target – 6
FILIP HELANDER: A shocking pass just at halftime summed up his team’s neglect but never really troubled too much and will have much tougher nights in the future – 6
CALVIN BASSEY : Big night for the youngster and he tried to throw a flood of crosses into the box and called for a penalty just before the break. Showed the desire that many lacked – 7
JEAN LUNDSTRAM: He looked like he was growing up in the game when he was cautioned and then made it worse with a second yellow card which was utterly preventable. Drop your team – 3
STEVEN DAVIS : Again, one of the few who tried to stay calm as anxiety mounted and in the second half he controlled the tempo of the game much more effectively – 7
JOE ARIBO : Didn’t have his usual influence in an offensive sense, but won a lot of balls in the first half when the team was struggling and resumed their performances after the break – 6
IANIS HAGI: Floated in and out of the game in the first half, but showed a lot more energy, desire and creativity after the break and he more than played his part when Rangers faced him – 7
ALFREDO MORELOS: Did next to nothing for an hour other than missing a great opportunity with a header, but when the next opportunity presented itself he kept a header to score the vital goal he desperately needed – 6
RYAN KENT : Hit the bar but should have scored and it was another night where next to nothing happened for a player who looks lacking in confidence and he did not reappear after the break – 4
SCOTT WRIGHT : For Kent at halftime and made a huge difference with his attitude, abilities and energy – 7
SCOTT ARFIELD : Replaced Aribo 10 minutes from the end – 2
CEDRIC ITTEN : Got the last seven minutes for Morelos – 2
STEPHEN KELLY : Injury time under for Hagi – 1