The 18-year-old Scot, who had been awarded a wild card, beat the Canadian Frederic Niemeyer 6-2, 6-4 and his chances of further progress were improved when his expected second-round opponent, the No 2 seed Justin Gimelstob, was beaten by the Australian Marc Kimmich, who qualified as a lucky loser for the Challenger event which is a level below the ATP tour.
While Murray's big serve came as no surprise to the crowd, his all-around game and skill did, and whether he was charging the net or at the baseline, Murray seemed to be able to return every Niemeyer shot.
"I've always been quick on the court," he said. "I've got good anticipation, and I feel quicker [on the hard court] than on grass. And this court is real bouncy, the ball comes up high. I'm happy because I told my coach I felt slow in practice."
As for his prospects of winning the event, Murray who reached the third round of Wimbledon this year on debut and went out of last week's Newport grass-court event in the second round, was characteristically level-headed. "All the guys I'll play have higher rankings than me," he said. "If I play the way I did today, I have a chance."
Elsewhere, in Houston, Steffi Graf made her first professional appearance since she retired six years ago, playing singles, doubles and mixed doubles in the World Team Tennis league.
The 36-year-old lost 5-3 in a tie-break to the Russian, Elena Likhovtseva, in her singles match for the Houston Wranglers. In the doubles, Graf and Ansley Cargill lost to Likhovtseva and Anna Kournikova 5-2. She did enjoy one win, however, combining with Mardy Fish to beat Kournikova and Mark Knowles 5-3 in the mixed doubles.