Top seed David Ferrer was also victorious 6-3 7-5 over Italy's Andreas Seppi, but second seeded Czech Thomas Berdych crashed out 6-3 6-2 against Spaniard Pablo Andujar.
The British number one claimed his second title of the season in Vienna last week and is hoping to boost his chances of reaching the World Tour Finals in London next month with another strong showing in Spain.
And despite looking far from sure on his own serve, the two-time Grand Slam champion had too much for Melzer to extend his head-to-head record over the world number 121 to 7-0.
"I like the conditions at this tournament, there is a nice climate and I come here now and again to practice indoors."
Murray is competing for the fifth straight week having also won in Shenzhen last month and is happy with how his form has progressed in the final part of the year.
"I have been improving throughout the season. I didn't start the year as well as I have been playing in the last three months when I have felt a lot better."
A similar pattern ensued in the second set with both players throwing their racquets in frustration as there were four breaks of serve in the opening seven games.
However, Murray made the decisive break to move ahead 5-3 and served it out despite having to save two break points. Next up for the Scot is a meeting with Italian Fabio Fognini in round two on Thursday.
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