Ally McCoist's men were dominant throughout, as Celtic's cause was not helped by red cards to Cha Du-Ri and Victor Wanyama, while manager Neil Lennon was also sent to the stand at half-time.
Carlos Bocanegra was also dismissed by referee Calum Murray, before Scott Brown pulled a goal back for the Hoops late on from the penalty spot and Thomas Rogne also netted in injury time.
As well as delaying Celtic's title celebrations, the win also allowed Rangers to avoid the unwanted record of a fourth consecutive home defeat for the first time in their 140-year history.
Rangers made five changes from last week's defeat to Dundee United with Steven Whittaker making his first appearance since December 24 after recovering from a groin problem, while Sasa Papac shrugged off a knock.
Defensive duo Bocanegra and Dorin Goian were back from suspension and Aluko was also drafted back in.
Celtic were without James Forrest, who missed out with an ankle injury, while Gary Hooper started on the bench after being rated doubtful with a dead leg.
Rangers had the best of the chances early on and Aluko's left-footed strike in the opening minutes was blocked for a corner by Cha.
Rhys McCabe then saw his shot from distance fizz past the post.
The breakthrough came after 11 minutes when Aluko showed impressive skill to take the ball past Rogne and then Charlie Mulgrew before rifling home from 12 yards.
Celtic could have been back on level terms within moments but Allan McGregor saved well from Georgios Samaras before the rebound from Anthony Stokes was deflected over the crossbar.
The Rangers goalkeeper then produced another decent save when he tipped a Stokes volley past the upright as the Hoops searched desperately for the leveller.
Goalscorer Aluko attempted to turn provider when he whipped a cross from the right into the path of Lee Wallace but the defender blasted harmlessly over.
At the other end, Brown picked out Stokes at the back post but his header was comfortably gathered by McGregor.
Celtic were dealt a further blow after 29 minutes when Cha was shown a red card by referee Murray for hauling down Wallace on the edge of the box.
Stokes was sacrificed for Emilio Izaguirre as Celtic made their first change a couple of minutes later but they had top be content going into the break 1-0 behind.
Lennon was not in the dug-out for the second half, with reports claiming he was sent to the stand at half-time.
The visitors then saw their numbers depleted further when Wanyama was dismissed after 57 minutes for a challenge on Whittaker.
Aluko sent the resultant free-kick just past the post, before setting up Lee McCulloch for a shot that was tipped over by goalkeeper Fraser Forster.
Rangers made their first change when the impressive McCabe was replaced by Kyle Lafferty after 60 minutes, as the Northern Irishman made his first appearance since January 2 after recovering from a hamstring tear.
Lafferty almost enjoyed a dream return to the action when he burst through on goal and found himself one-on-one with Forster only to see his point-blank shot saved well by the goalkeeper.
But Forster was picking the ball out of the back of the net after 72 minutes.
He again saved a Lafferty effort but the ball broke for Andy Little - who had replaced Aluko seconds earlier - to stab home from close range.
Any hopes of a Celtic comeback were dashed when Wallace lashed home a left-foot drive six minutes later..
There was further drama with two minutes to go when Bocanegra was sent off for a foul on Samaras and Brown converted from the penalty spot.
Rogne then bulleted a header past McGregor in injury time but it was too little too late for Celtic.