Anders Nilsson made 27 saves for Ottawa.
"I think we played a full 60-minute effort and we didn't give them a whole lot," Nilsson said. "Obviously they have some skilled guys that generate some chances for them, but other than that ... we deserved to win tonight."
Lundqvist, who last won on March 9 and has two wins since Feb. 1, remained at 449 NHL wins, five behind Curtis Joseph for fifth in history. The Rangers have two regular-season games remaining.
"I don't know if I deserve to play," Lundqvist said. "[Backup Alexandar] Georgiev has been winning, he's been playing really well. I'm not finding ways to get wins here. It's been a draining few months here not getting it done."