The world No.3 was in impressive form against his inspired opponent and eventually took the first set 6-4 after a quality 1 hour and 5 minutes of tennis.
Muller played an intelligent game, pushing Murray on every opportunity; defending his serve at multiple break points and fighting hard in the third game, which lasted over 20 minutes.
True to form the set-winning break game took over eight minutes as the pair exchanged blows and set points numerous times.
Murray broke in the third game of the second set taking firm grip on the match, his ball-striking looking particularly sharp, and seemed set to clinch victory when he served for it at 5-4. But a double fault proved costly as the??left-handed player clawed his way back into the game after??benefiting from two net cords to at 5-4 down with his first break of Murray’s serve.
Muller couldn’t maintain the momentum and the Scotman immediately broke back to make it 6-5. Murray made no mistake at the second time of asking and wrapped up the match with a love service game.
He will play Portugal’s Joao Sousa in the next round. Sousa dispatched??Ireland’s James McGee in straight sets on Monday.??Murray has beaten Sousa in straight sets in??all four of their previous meetings, most recently at last month’s Australian??Open.
There was disappointment, though, for British number two James Ward, who lost 6-4 6-4 to sixth seed Feliciano Lopez.
Ward came through qualifying to reach the main draw but could not pull off the??upset against the world number 13 and was left to rue eight missed break??points.
Londoner Ward will now begin his preparations for next weekend’s Davis Cup??clash against the USA in Glasgow having on Tuesday been named alongside Murray??in the Great Britain team.
Afternoon session results:
Tomas Berdych (CZE x4) bt Jeremy Chardy (FRA) 7-6(7-2)
Sergiy Stakhovsky (UKR) bt Lukas Rosol (CZE) 4-6, 6-1, 6-4
Marsel Ilhan (TUR) bt Alexander Zverev (GER) 6-1, 7-6(7-4)
Simone Bolelli (ITA) bt Lucas Pouille (FRA) 6-3, 6-3
Feliciano Lopez (ESP) bt James Ward (GBR) 6-4, 6-4
Borna Coric (CRO) bt Malek Jaziri (TUN) 5-7, 6-3, 6-3
Roberto Bautista (ESP x7) bt Dominic Thiem (AUT) 6-3, 6-2
Andy Murray (GBRx3) bt Gilles Muller (LUX) 6-4, 7-5
Marcos Baghdatis (CYP) bt David Goffin (BELx8) 6-2, 7-5