Anze Kopitar had a goal and two assists, and Jack Campbell made 22 saves for the Kings (18-26-5), who have lost three straight and are 1-5-1 in their past seven.
"It's the desperation part that kicked in in the third period, second half of the third," Kopitar said. "We've got to figure out how to bring that to the start of games."
Driedger was starting in place of Sergei Bobrovsky, who missed a second game because of a lower-body injury he sustained in practice Saturday. Montembeault was recalled from Springfield of the American Hockey League under emergency conditions Sunday and Wednesday.
"I've been running around a lot," Montembeault said. "I had three flights in three days: Sunday, Monday, Tuesday. At least I had a chance to get a good practice yesterday and I skated this morning too. Obviously I wasn't expecting to play in that one, but it turns out we played very well and we had a good win."
Dadonov gave Florida a 1-0 lead with a power-play goal at 6:04 of the first period. He redirected Jonathan Huberdeau's pass to the front of the net after every Florida player touched the puck on a passing sequence.
Frank Vatrano made it 2-0 at 3:06 of the second period when he one-timed Dominic Toninato's drop pass at the top of the right circle.
"We did good on the power play, we had one of those long goals that's really special," Quenneville said. "I think everyone touched it at least once. We moved it around crisply and had a nice finish to it. [Toninato's] pass over to Frankie was a perfect pass and a nice goal as well. After that, we're in a pretty good spot. We have to make sure we close that out in a better way."
Matheson made it 3-0 at 4:55 of the third period with a slap shot from the point, and Brian Boyle scored at 7:06 to make it 4-0.
Alex Iafallo made it 4-1 when he scored on a deflection at 11:42. Jeff Carter and Kopitar each scored a power-play goal, at 15:08 and 17:20, to get Los Angeles within 4-3.
"We were pretty sluggish right off the bat," Kings defenseman Drew Doughty said. "Just some mental mistakes. We weren't playing well right off the bat, and that's what set us off on the wrong foot and then we were chasing the game from there. But with 10 minutes left, [coach Todd McLellan] just kind of said, 'It's 4-0, let's start doing things right, setting up for the next game,' and we almost came back. I actually thought we were going to come back. We were close there. Good fight till the end, but not a good 60 minutes."
