Murray, the defending champion and No. 3 seed, claimed his first match win at Queen's in 2005 and went on to win the Wimbledon warmup three times.
But he failed to take advantage of eight set points after leading the first-set tiebreaker 6-2, and Stepanek survived to convert with his second set point.
A break to lead 1-0 in the second set put Stepanek firmly on the road to victory, and a further break to lead 5-2 left him serving for only his second win over Murray in seven meetings.
Murray's last defeat on grass was against Roger Federer in the 2012 Wimbledon final. Since then, he had won the 2012 London Olympics which was played at Wimbledon, and the 2013 Queen's and Wimbledon titles.
''I have only got myself to blame that I lost the first set,'' Murray said. ''I don't know how many set points I had, but quite a lot of them were on my serve. On this surface, especially, you shouldn't really be losing sets like that. For me, that's what's disappointing really about the match.
''And then, yeah, unfortunately got broke in the first game of the second set. I couldn't quite get it back.''
Despite his defeat, the Roland Garros semifinalist has no concerns as he heads toward the defense of his Wimbledon title.
''I don't think so,'' he said. ''I need to spend time on the courts practicing some things. You know, the difference between this year and last year is I played a lot of matches the last couple of weeks at the French Open. Since the Monday before the French Open, I have played every single day bar one up to now.
''Last year, I probably had about a week, 10 days preparation on the grass before I started here. This year, I had two days. I'm going to take a couple of days off, watch some of the World Cup.''
Top seed and Australian Open champion Stanislas Wawrinka took just 50 minutes to ease past American Sam Querrey 6-2, 6-2, and second-seeded Tomas Berdych overcame solid resistance from Frenchman Adrian Mannarino, winning 7-6 (2), 6-4.
Mannarino fought off 17 break points, including four set points at 6-5 in the first set, before Berdych broke on his 18th break point to lead 2-1 in the second.
Berdych will next face Feliciano Lopez after the Spanish left-hander defeated Frenchman Kenny De Schepper 7-6 (3), 6-7 (4), 7-6 (3) in a match with no breaks of serve.
Fifth seed and 2011 finalist Jo-Wilfried Tsonga was beaten 6-2, 6-4 by Marinko Matosevic. The Australian, who reached the final of a grass-court challenger last week and upset 2012 champion Marin Cilic in the first round, is coached by Hall of Famer Mark Woodforde
There were victories, too, for fourth-seeded Grigor Dimitrov of Bulgaria, who defeated Edouard Roger-Vasselin of France 7-6 (3), 6-4, and seventh-seeded South African Kevin Anderson who edged Ukraine's Sergiy Stakhovsky 6-3, 3-6, 7-6 (4). Eighth seed Alexandr Dolgopolov of Ukraine advanced 6-4, 4-2 when Jarkko Nieminen of Finland retired injured.