Dougie Imrie’s reply in the closing stages made it a far less comfortable win than it should have been for Rangers who are now eight points behind leaders Celtic at the top of the Premiership, having played three games more than the champions.
It was an especially gratifying night for Waghorn, making his first starting appearance for the Ibrox side since 14 October. His opening goal a minute before half-time was his first since September which he quickly added to early in the second half.
Rangers missed a host of chances to make the game safe before Imrie’s strike set up a tense finale which saw Accies threaten to snatch a point.
The narrative of Rangers’ Premiership campaign has been of a struggle for sustained momentum ever since they dropped two points at home to Hamilton on the opening day of the season.
Victory in this return fixture was a must if Warburton’s men were to find the kind of impetus required to keep Celtic’s coat-tails even remotely in sight beyond the turn of the year.
Waghorn’s goal was their reward for a steadily increasing spell of pressure in the closing phase of the first half but they were made to work hard for any sense of ascendancy in the contest by an Accies side in their customary committed and tactically diligent mood.
The first sight of goal for Waghorn came after just three minutes and there was an element of rustiness about his stabbed shot wide after being picked out by Barrie McKay’s driven cross.
The home side responded through some intelligent, probing play by Danny Redmond. His dangerous cross from the left was just too strong for Alex D’Acol to connect with, allowing Wes Foderingham to gather gratefully.
Rangers were finding it difficult to establish any significant tempo and rhythm on the artificial surface, but their first genuinely cohesive move of the night saw Lee Hodson link up well with Waghorn and Jason Holt before driving in a shot which Garry Woods held after an initial fumble.
The Hamilton keeper endured another uncomfortable moment when a long throw from Lee Wallace was flicked on by Danny Wilson. Woods’ unconvincing attempt to save saw the ball hit the top of the crossbar before he managed to clear the danger under pressure from Holt.
Frustration at a lack of clear-cut openings then got the better of Wallace who skied an ambitious 25-yard shot well off target.
There was a let-off at the other end for Rangers in the 34th minute. James Tavernier, attempting to shield the ball and let it run out of play, lost possession to Greg Docherty inside the area. The Accies midfielder might have done better to square the ball to a team-mate but fizzed a shot just wide from a tight angle.
Rangers responded to that scare by mounting the sustained period of pressure which culminated in Waghorn’s breakthrough. They were twice denied by two excellent pieces of defending from Michael Devlin. The Accies captain first made a superbly timed tackle to prevent Holt getting on the end of McKay’s clever reverse pass, then reacted sharply to block a netbound Waghorn shot.
As Rangers finally began to move through the gears, Holt saw a low shot diverted wide by Woods. The midfielder was a lively presence for the visitors and he duly provided the assist for the opening goal.
Holt darted to the byline on the left and picked out Waghorn with a lofted cross. The big striker’s header soared over Woods and went in off the underside of the crossbar.
Rangers picked up where they left off on the resumption, immediately getting on to the front foot, and doubled their lead seven minutes into the second half. It was a well constructed goal with McKay’s perfectly weighted pass finding Wallace on the left of the Accies area. His cross found Waghorn unmarked for a confident close-range finish.
Rangers were now creating openings almost as they liked, Tavernier saw a shot blocked by Woods, then Joe Garner came close with a well struck effort from around 25 yards.
Tavernier wastefully blazed a shot over and it suddenly looked as if Rangers might pay for their profligacy when Accies halved their deficit in the 77th minute. Andy Halliday was caught in possession by Redmond and his low cross from the left was tucked home from close range by Imrie.
Georgios Sarris and Ali Crawford came close to grabbing an equaliser but Rangers managed to see out a victory they merited over the piece.