The world number three, competing in a tournament for the first time since winning his maiden grand slam at the US Open last month, was in control early on but had to battle to win 6-2 3-6 6-2 as Wawrinka pushed him all the way.
The Swiss beat Murray at Flushing Meadows in 2010 and despite his record since then reading 0-13 against the big four of Roger Federer, Novak Djokovic, Murray and Rafael Nadal, he still possesses the tools to challenge the game's leading lights.
Yet early on it was largely plain sailing for Murray with two breaks giving him the opening set with Wawrinka wasting the opportunities which came his way.
Wawrinka was more ruthless in the second as his big forehand started to clean the lines.
His first chance to edge ahead came with Murray serving at 1-2 and despite saving two break points, Murray was unable to stave off a third as Wawrinka powered in another big forehand.
The Scot almost replied instantly but Wawrinka held on thanks to some big serving and then ran through the rest of the set without alarm to level matters.
The match hinged on the fourth game of the final set with a combination of brilliance and extreme fortune handing Murray a break and a 3-1 lead.
The top seed saw three break points come and go as Wawrinka raised his aggression levels to serve his way out of danger.
But the Swiss was powerless when Murray set up a fourth as a forehand return struck the top of the net before dropping over.
Warwick's frustration was evident as he smashed a racket early in the next game but he could not channel it into a comeback and Murray broke again to wrap up the match in two hours and a minute.
He next meets big-hitting Canadian Milos Raonic, who earlier beat Janko Tipsarevic in a third-set tie-break.