The 20-year-old Scot, who missed over three months of the season with a wrist injury, put the Czech to the sword with the help of an impressive array of passing shots to earn himself a second-round match against 15th-seeded Argentine Juan Ignacio Chela.
Murray, who signalled his return to form by reaching the final in Metz earlier this month, made a sharp start, despite spurning three break points in the second game.
He looked steady on his own serve and after putting Stepanek under heavy pressure he broke in the 10th to take the first set 6-4.
He continued to stretch the Czech around the court in the second and raced his way into a 5-0 lead before closing out the match on his own serve.
"That's probably one of the best matches I've played, not just since I've been back from injury, but since I've been on tour," Murray told a news conference.
"I think I have played 10, 11 matches or something since I came back from injury, which isn't a lot really, so to be playing like that in so few matches is really good.
"I think I showed that if I can keep that level of consistency up throughout the tournament I am going to have a good chance of beating the best players."
BATTLED BACK
Qualifier Robby Ginepri came from a set down to defeat Austria's Jurgen Melzer 2-6 7-6 6-4 on Monday and book himself a daunting match against defending champion Roger Federer.
The 25-year-old American, who lost to Federer in straight sets in the quarter-finals of last year's tournament, battled his way back from a stuttering start to edge the second set on a tie-break and maintain his 100 percent record against Melzer.
Former Australian Open finalist Marcos Baghdatis will meet number two seed Rafael Nadal after the Cypriot clinched a 6-3 4-6 6-1 win over Romanian qualifier Andrei Pavel.
Fernando Verdasco breezed his way to a 6-1 6-1 victory over fellow Spaniard Alberto Montanes and now faces third seed Novak Djokovic who won in Vienna at the weekend.
Juan Monaco recovered from a set down to win through 6-7 6-0 6-4 against Russia's Igor Andreev on his debut and set up a second round clash against 11th-seeded German Tommy Haas.
Another Argentine, wild card Juan Martin del Potro, wrapped up a high-speed 7-6 6-1 victory over Italy's Potito Starace, while Croatia's Mario Ancic cruised to a 6-4 6-2 win over Marc Giquel of France.
Austrian qualifier Stefan Koubek came through 6-3 3-6 6-4 to claim his first win in three attempts against Jarkko Nieminen of Finland.