Kilmarnock secured a fifth-place finish in the SPL with their first win at Ibrox since October 2000.
Naismith (left) cracked in a wonderful goal at Ibrox
The well-organised and industrious visitors frustrated their lethargic hosts in a tepid first half.
And Steven Naismith popped up to steer in a sweet strike on the half-volley from 16 yards early in the second half for his 18th goal of the season.
Killie keeper Alan Combe was busy in the closing stages but Walter Smith's men could not find a way through.
Departing Rangers duo Dado Prso and Stefan Klos were both denied the opportunity to take part in their last ever game at Ibrox.
Prso suffered an ankle injury in training on Friday and Klos missed out with a dislocated thumb.
Alan Hutton was suspended, meaning Ian Murray was drafted in to fill the void at right-back.
Kilmarnock made three changes after defeating Hibernian last week, with Gary Locke, Momo Sylla and Aime Koudo getting a chance at Ibrox.
The atmosphere inside the stadium was flat throughout a dull first half as the home side struggled to raise their game for a largely meaningless encounter.
In the opening minutes Naismith could have taken advantage of an Allan McGregor slip when he burst through on goal but the Rangers goalkeeper recovered in time to clear the danger.
Rangers skipper Barry Ferguson then latched on to a long ball and unleashed a threatening effort from 20 yards but the shot dipped just over the crossbar.
McGregor was called into action again to block a Gordon Greer header, after the Killie defender connected well with a Locke free-kick.
With Murray taking every opportunity to get forward from defence, Rangers enjoyed a spell of concerted pressure but all they could muster was a Charlie Adam shot that went high over the bar.
Rangers introduced Chris Burke after the break and the winger immediately burst into the penalty area, only to toe-poke a shot narrowly wide.
The visitors went ahead after 53 minutes when Grant Murray delivered to the unmarked Naismith and the 20-year-old cracked home a neat half-volley from the edge of the penalty area.
Adam, who has a fine record from set-pieces this season, curled a 25-yard free-kick in the direction of the top corner but Combe did well to clutch the shot.
Rangers substitute Steven Lennon then fashioned a strike with a neat turn in the penalty box but shot straight at the keeper.
Naismith was only a yard away from doubling his tally on 76 minutes when he lashed a 20-yard strike wide of the target, with McGregor motionless.
The lively Lennon fired in a fierce shot after the ball broke to him on the edge of the penalty area but Combe was again equal to it.
Kilmarnock were forced deeper and deeper as Rangers poured forward in the closing stages and held on for a rare success in Glasgow.
Rangers: McGregor, Murray (Shinnie 82), Ehiogu, Weir, Papac, Ferguson, Hemdani (Burke 46), Thomson, Novo (Lennon 66), Boyd, Adam. Subs Not Used: Robinson, Svensson, Rae, McMillan.
Booked: Adam, Novo.
Kilmarnock: Combe, Grant Murray, Greer, Frazer Wright, O'Leary, Sylla, Fowler, Locke (Hamill 89), Koudou (Di Giacomo 66), Nish, Naismith. Subs Not Used: Harpur, Hay, Dodds, Gibson, Quinn.
Booked: Grant Murray, O'Leary, Nish.
Goal: Naismith 53.
Ref: I Brines