Defending champion Rafa Nadal's progress was quicker. The Spaniard, aiming for a record seventh French Open title, thrashed Uzbekistan's Denis Istomin 6-2 6-2 6-0.
Nadal and Murray were joined in the third round by French fifth seed Jo-Wilfried Tsonga, who returned to complete a match suspended overnight because of rain and finished off German Cedrik-Marcel Stebe 6-2 4-6 6-2 6-1.
Local favourite Paul-Henri Mathieu took the hardest route. He set a French Open record for the most games played in a match (76) when he beat American John Isner 6-7 6-4 6-4 3-6 18-16 in five hours 41 minutes.
Isner is no stranger to long matches, needing 183 games to beat Mathieu's compatriot Nicola Mahut at Wimbledon two years ago in the longest professional tennis match ever played.
Murray was a semi-finalist last year, his best result at the claycourt grand slam, but looked to be heading for an early exit in the first set of his match on Philippe Chatrier court.
He summoned the trainer three times and lay, with his teeth clenched, as his back was massaged, then got up again to move stiffly around the court. At changeovers, he stayed on his feet rather than sitting down.
Nieminen, however, was unable to take advantage and as the match progressed, and Murray loosened up and started going for more shots, the 48th-ranked Finn began hitting unforced errors.
When he hit a backhand out to give Murray breakpoint at 2-4 in the fourth set, Nieminen dashed his racket to the ground and stamped on it. His next action was a double fault and Murray found himself serving for the match.
Though Nieminen saved one matchpoint with a winning service return, Murray hit a service winner on the second and will now play Colombian Santiago Giraldo, who knocked out 25th seed Bernard Tomic of Australia 6-4 6-1 6-3.
Murray said his problem was probably a back spasm and, with the sanction of his physiotherapist, he planned to play on.
"I'm not doing myself any actual damage by playing with what I have," he told a news conference. "I have had all the best advice from some of the top surgeons and physios. I'm confident that I'm doing the right thing."
NINE GAMES
Nadal has lost only nine games in the first two rounds here but, after spending less than two hours on the Suzanne Lenglen court, said he still had things to work on despite his impressive form.
"Sure, I can improve things. The serve is the first one. I think I improved the level of my serve during the match but I started the match serving bad. That's the thing I can improve a little bit."
Nadal, who has won on clay in Monte Carlo, Rome and Barcelona this season, now faces Argentine qualifier Eduardo Schwank.
Tsonga had gone off court on Wednesday evening level at one set all and 1-1 in the third with Stebe when rain fell on Roland Garros for the first time this week.
The Frenchman started Thursday with a break and needed less than an hour to see off Stebe and set up an appointment with Italian Fabio Fognini.
Tsonga was delighted that rain had cut short Wednesday's play, saying he had had trouble concentrating.
"It was children's day yesterday - there was a lot of noise, and I was getting a bit crazy," he told a news conference. "So I think it was a good idea the match was stopped yesterday and I could start again in far better conditions for me."
Sixth-seeded Spaniard David Ferrer had a straightforward, 6-3 6-3 6-2 win over French player Benoit Paire and will now play 27th seed Mikhail Youzhny of Russia.
Women's fourth seed Petra Kvitova, who has had a year marked by illness and injury, was in fine form on the Suzanne Lenglen court, swiftly beating Pole Urszula Radwanska 6-1 6-3.
Defending champion Li Na enjoyed her second straight-sets win when she sped past Frenchwoman Stephanie Foretz Gacon 6-0 6-2 while former world number one Caroline Wozniacki was nearly as quick in beating Australia's Jarmila Gajdosova 6-1 6-4.
Frenchwoman Virginie Razzano, who knocked out pre-tournament favourite Serena Williams in the opening round, lasted only one more round, losing 6-3 7-6 to Arantxa Rus of the Netherlands.
Another local favourite Arnaud Clement, the oldest man in the draw at 34, bade goodbye to Roland Garros after 15 appearances with an emotional ceremony on court after his 3-6 7-6 0-6 6-2 6-1 defeat by Belgian lucky loser David Goffin.
Former Davis Cup captain Guy Forget and French tennis federation president Jean Gachassin presented Clement with a glass cube containing a sample of the Roland Garros clay.
