Japan's Taro Daniel achieved a straight set victory against Murray in the second round of the Australian Open last month, but the pair's recent meeting told a different story.
After a cagey start to the match, Murray clinched the first break to go 4-2 ahead in the opening set.
With momentum behind him, Murray dominated the following two games to win the first set 6-2.
Daniel responded well in the second set, with the world No.114 immediately breaking Murray, before the Scotsman fought back level.
Murray then held his serve and managed two further breaks, sealing the match in one hour and 20 minutes with another 6-2 set.
Having won the Qatar Open twice before, Murray's win takes him to the last 16 where he'll face second seed and runner-up in last year's tournament Bautista Agut in Doha.
It'll be an emotional matchup for the 34-year-old, after he lost to the Spaniard in the 2019 Australian Open - a match many believed was his last.
However, three years on, the former world No.1 is still in action following career-saving hip surgery.
Murray only entered the tournament as a late wildcard, but is slowly inching closer to achieving a remarkable 700 career wins.
He returns to action on Wednesday afternoon, with his round of 16 clash scheduled to start at 15:00 GMT on Centre Court.