Boyd completed a blistering move after Dado Prso and Thomas Buffel had prised open the defence allowing him to blast the ball high into the empty net from five metres out in 36 minutes for the opener.
Hibs levelled with an own goal from Rangers' Brahim Hemdani in the 72nd minute but Boyd flicked home the winner just a minute later into the far corner.
Third-placed Rangers now have 70 points from 37 matches while second-placed Hearts, with 71 from 36, can secure the Champions League slot by beating Aberdeen at home on Wednesday. Dundee United were beaten 1-0 by Dunfermline in the other Premier League fixture on Tuesday.
Champions Celtic, with 87 points from 36 matches, play Kilmarnock on Wednesday while Inverness Caley Thistle face Falkirk and relegated Livingston tackle Motherwell.
"I didn't believe he would do so well and it is a credit to him to come to Rangers and show the mental toughness he has done to hit the ground running," manager Alex McLeish told BBC radio.
"It can take a lot of players time to settle in. But, his goal record is incredible, phenomenal."