Fiorentina were always up against it after striker Alberto Gilardino was sent off on the stroke of halftime for elbowing midfielder Jeremy Toulalan.
Lyon, though, could not break through until the 76th minute when Bosnia midfielder Pjanic struck from close range.
"We had to go for it and it was not easy," Lyon coach Claude Puel told reporters. "The referee (Dutchman Pieter Vink) didn't help us by letting them commit many fouls in midfield that stopped us from creating chances."
"We needed to stay calm and we managed to do that. There is a strength, a spirit in that team I like, even if it would have been better to score one more goal."
Fiorentina coach Cesare Prandelli said: "There's no need to comment on Gilardino's sending off. He had no intention to hurt and was just going for the ball.
"It's a pity because until it happened we were looking good."
BASTOS INJURED
The home team, in their 10th consecutive Champions League campaign and hoping to go beyond the quarter-finals for the first time, saw Brazilian midfielder Michel Bastos limp off after 26 minutes.
Lyon struggled early on against physical opponents and hardly created a chance during a lacklustre first half.
The second period was slightly better with a couple of opportunities for Lyon's energetic Argentine striker Lisandro Lopez, who almost scored when his header was well saved by keeper Sebastien Frey eight minutes from time.
Overall, the crowd at the Gerland stadium witnessed a relatively dull affair featuring six yellow cards.
The two teams also met in last year's group stages, Lyon drawing 2-2 at home before winning 2-1 in Italy to go through to the knockout stages.
