Carlos Vela, the 2019 MLS MVP, made his second start of the season and assisted on Rossi's second goal after missing three games with a leg injury.
After beginning the weekend last in the Western Conference, the victory moves LAFC up to ninth in the West table, even with Real Salt Lake on points but behind on goal difference.
Michael Barrios scored his first goal for Colorado in his sixth game for his new club after six seasons with Dallas.
But the Rapids saw their three-match winning streak snapped on a night they were deserving losers. They now sit fifth in the West, six points off leaders Seattle, which plays on Sunday afternoon.
Los Angeles led Colorado 17-11 in shots and 5-2 in efforts on target, and held nearly three-fifths of the possession time.
Rossi now has three goals on the season, a year removed from the 14 he scored to win the 2020 MLS Golden Boot.
He gave the hosts the lead after 14 minutes.
Baird sliced past a couple defenders on the dribble, then guided a diagonal ball to Rossi, who finished low inside the left post with his first touch, giving goalkeeper William Yarbrough little chance.
Vela was at the heart of Rossi's second goal 19 minutes later, taking an innocent looking pass from Tristan Blackmon in midfield, weathering a challenge and taking the ball forward, then finding Rossi inside the penalty area.
Sisniega saved another 1-on-1 against Barrios not long after, which proved to be the Rapids best chance to equalize over the final 40 minutes and their final shot on goal.