The three-time Grand Slam champion raced through the first set but was made to dig deep by his French rival in the second to finally get his 2024 season off the ground.
Backed by vociferous support in Doha the 36-year-old Scot conjured up a couple of sublime drop shots, including in the tense tie-break, to win for the first time since last October.
How much the success meant to last year's beaten finalist, now ranked 50th in the world, was clear when he raised his arms in triumph, exclaiming "Yes".
"The last few months have been really tough on court for me. It was getting tight at the end there, I'm delighted to get through," the Doha winner in 2008 and 2009 said courtside.
"I'm proud I managed to get through the match, and happy for my team who have been working hard with me to get through this difficult moment.
"Hopefully this is the start of a better run."
In the second round he comes up against an unknown package in the shape of 18-year-old Czech Jakub Mensik, who sent fifth-seed Alejandro Davidovich Fokina packing 7-6 (7/3), 6-4.
"He's obviously a very promising young player with a huge serve," said Murray.
"He moves well for a big guy, new on tour, I'll need to be ready for that," he added.
Last month Murray hinted that retirement may not be far away after a poor run, following a comprehensive first-round Australian Open defeat by Tomas Martin Etcheverry.
