The first set on Court Suzanne Lenglen was a horror show for the world number one against a player who almost skipped Roland Garros because of a calf injury.
But Murray turned things around to win 6-7 (3/7) 6-2 6-2 7-6 (7/3) and set up a third-round clash against former US Open champion Juan Martin Del Potro.
It is tough to see Murray winning that one without a significant improvement in his form, although Del Potro was struggling physically before second-round opponent Nicolas Almagro was forced to retire with a knee injury.
After three hours and 35 minutes on court, Murray said: “I expected it to be very tough. He (Klizan) goes for huge shots and on his forehand, he can hit winners from anywhere.
“Sometimes you think you’ve hit a good shot and he comes up with unbelievable power. It’s very tough. I tried to play solid, as the match went on I tried to hit the ball deeper and was controlling more of the points.”
Murray finished his first-round match against Andrey Kuznetsov with a run of eight games in a row and with the mood cautiously optimistic.
Having arrived in Paris short of wins and confidence, Murray was hoping the best-of-five-set format and relatively kind draw would allow him to play himself into form.
But any confidence he had gained swiftly evaporated in the early afternoon sunshine as Klizan, ranked 50th, took an early hold on the match.
Muttering about his movement, Murray was passive and error-strewn, allowing his opponent to dominate with his big forehand.
Murray looked to have turned a corner when he broke Klizan as he served for the first set at 5-4 but the Scot then played an awful tie-break.
Even when he won the second set with a run of five straight games, there were plenty of alarm bells ringing.
Klizan’s play had become a lot more erratic, the 27-year-old no longer finding the mark so often with his forehand and appearing bothered again by his calf.
Murray extended his winning streak to seven games at the start of the third set and and finally seemed to be finding a bit of rhythm.
Two points in the opening game where he turned defence into attack were reminiscent of Murray at his best but, although he took the set, we were still a long way from that.
Klizan had infuriated his previous opponent Laurent Lokoli to such an extent that the Frenchman refused to shake his hand. Apparently close to retirement one minute, Klizan recovered from dropping the fourth set to love to win in five.
Murray had said he would be ready for any such antics but the world number one was consumed by his own frustration as he got bogged down in the fourth set.
Chuntering away to himself, his box and the umpire, Murray lost the first three games despite having chances to win all of them.
Klizan veered from appearing to be on his last legs one minute to sprinting full pelt the next, producing some fine shots when he most needed them and torturing Murray with drop shots.
But, as in the first set, he could not serve it out, and Murray should have made it two straight breaks in a long 11th game.
He continued to do things the hard way but Klizan’s resistance finally came to an end in the tie-break and Murray took his second match point with one of his best shots, somehow digging out a forehand winner.