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Murray, seeded second, arrived in London after sustaining an ankle ligament injury during his run to the French Open semi-finals that briefly threatened his participation in a tournament he won in 2009.
But with the start of his home Grand Slam at Wimbledon just 11 days away, Murray, who was given a first-round bye, will be encouraged that he was able to last the distance in a tough test against the experienced Malisse.
Although this was hardly a vintage display from the British No 1, he had no obvious problems with his ankle and showed plenty of spirit to set up a clash with Serbian 14th seed Janko Tipsarevic.
Australian Open finalist Murray had spent the previous three days practising at Queen's to test out his ankle and reacquaint himself with the unique demands of playing on grass afer his clay-court campaign ended in a defeat by Rafael Nadal at Roland Garros.
It was clearly time well spent as the 24-year-old Scot took control with a break in Malisse's first service game.
Despite wearing a strapping on the ankle, Murray was moving well enough and some wayward ground-strokes from Malisse allowed him to build a 3-1 lead before a brief rain delay.
Murray had to save two break points following the resumption and after that fright he swiftly finished off the set.
However, Murray found it much harder to take control in the second.
He finally raised the tempo at 5-5 and amassed three break points, only to see world No 40 Malisse save them all.
Murray's failure to convert those chances seemed to rattle him and a succession of unforced errors in the next game presented Malisse with two set points and the Belgian took the second to level the match.
Malisse - a Wimbledon semi-finalist in 2002 - and partner Ken Skupski had beaten Murray and his brother Jamie in the doubles on Tuesday.
But Murray ensured there would be no repeat as, aided by a pair of wild forehands from Malisse, he broke for a 2-1 lead at the start of the final set.
He had to save two break points at 3-2 and that was Malisse's last chance as Murray served out the match.
Next up for Murray is the talented but erratic Tipsarevic, who defeated American Michael Russell 7-6, 7-6.
Elsewhere in the second round, South Africa's Kevin Anderson set up a third-round clash with four-time champion Andy Roddick after a 6-2, 6-4 win against American youngster Donald Young.
Johannesburg-born Anderson, seeded 15th, was quickly into his stride against the 21-year-old left-hander.
Two breaks of Young's serve easily sealed the first set and it took just one break to take the second set after a rain delay.
Croatian eighth seed Marin Cilic eased through to the last 16 with a 6-4, 6-4 win against French qualifier Arnaud Clement.
Clement, 33, had won their last grass-court meeting at Wimbledon in 2008, but Cilic was always on top this time as he saw off the oldest man in the draw in convincing fashion.
