Northern Ireland international heads home the only goal of an entertaining encounter as the home side eventually feel the effects of Johnny Russell's first half sending off
An open game looked like it would prove a formality for the away side when Johnny Russell was sent off after a clash with Kirk Broadfoot in the first half, but Ally McCoist’s side had to survive a couple of scares after Lafferty had edged them in front in the second half.
Steven Naismith partnered the Northern Ireland forward in attack in the absence of star striker Nikica Jelavic, who missed out with a knee injury picked up on international duty last week. New signing Matt McKay, who completed a move from A-League side Brisbane Roar for around £300,000, was included on the bench.
Lauri Dalla Valle was handed his debut for the home side in attack while fellow Fulham loanee Keanu Marsh-Brown was among the substitutes.
After an encouraging start, Russell left his United teammates with an uphill battle after appearing to make a headbutting motion towards Broadfoot when the pair clashed after a Russell foul.
But Rangers struggled to capitalise of their man advantage. The two teams went in with the scores level at the break, a Naismith shot wide after a penetrating run about the closest the Glasgow side came.
15 minutes in to the second-half, Lafferty grabbed the decisive goal. Gregg Wylde’s pinpoint cross to the back post was powerfully headed back across goal by the former Burnley man and beyond goalkeeper Dusan Pernis.
Steven Davis had a glorious chance to extend the lead ten minutes later when he broke through on goal and, one-on-one with Pernis, placed his left-footed shot past the Slovakian only to see it bounce off both posts and away.
Doran Goian came close from the resulting corner and another Naismith effort was cleared off the line by defender Garry Kenneth but it was Peter Houston’s side that began to exert some late pressure in an attempt to salvage a point.
After Danny Swanson’s long-range effort just missed John Rankin came agonisingly close to levelling the scores, shooting inches wide after a corner had been headed out to the edge of the Rangers box.
Allan McGregor held firm in the Rangers goal during a series of late corners to preserve the narrow lead and send his side, at least temporarily, three points clear at the top of the pile.