The world No 1 arrived in Paris short of form and confidence and nursing a heavy cold after only four wins since February.
Russian Kuznetsov, ranked 73, would not normally have been seen as a major danger, but the usual expectations around Murray have been significantly tempered.
The Scot showed why he has been struggling in the second set, allowing Kuznetsov to dictate and aiming sarcastic grins and applause at his box.
But a remarkable point early in the second set put him on the right course. Chasing a lob that looked certain to win the point, Murray somehow hooked it back over his shoulder, Kuznetsov netted the smash and the top seed went on to win 6-4 4-6 6-2 6-0.
“It was a good get,” said Murray. “When the lob went up, I thought that I wouldn’t be able to reach it, but I did.
“I think he made a couple of simple errors after that. I got the break, and then obviously didn’t look back from there.
“It definitely got better as it went on. I started to move a bit better towards the end. I was hitting the ball better when I was defending. That’s something the last few weeks I haven’t done so well and didn’t start off the match doing particularly well.
“But once I was getting a little bit more on my ball when I was defending, there weren’t too many openings for him in the points. It was a decent start, considering obviously how I played in the build-up.”
The first set was a mixed bag. Murray held onto his serve having lost the opening three points of the match then broke the Russian to lead 4-2. A poor game when he was serving for the set was swiftly cancelled out by a break to love.
Kuznetsov is a slight figure, but can generate surprising power with his flat hitting and has had a good clay season, reaching the semi-finals of the Geneva Open last week. From 2-1 down in the second set, he won four games in a row and, although Murray retrieved one break, the Russian served out the set at the second attempt to level the match.
The contest looked like it could go either way, but, once Murray took control, he showed the sort of ruthlessness that bodes well for the tournament.
In the fourth set, the 30-year-old toyed with his opponent, pulling him forward time and again with drop shots as he reeled off eight games in a row to finish the match.
Murray said: “Some of the shots towards the end of the match, it’s obviously a lot easier to play them when you’re two sets to one up and 4-0 or 5-0 up; it’s a bit easier to have the freedom to try a drop shot or a lob or a big return.
“It’s a bit different doing it at that stage than at 4-4 in the first set. But it was good towards the end. It was better. I still think I can do some things a bit better than I did, obviously.
“I will try to keep that going. I was just trying to find a way to get through, and as efficiently as possible.
“I did that in the end.”
The Scot will next face Slovakian Martin Klizan, who won a bad-tempered encounter with French wild card Laurent Lokoli 7-6 (7/4) 6-3 4-6 0-6 6-4.