Steel gave the Ducks a 1-0 lead 2:23 into the second period when Jakob Silfverberg's pass into the crease caromed off Steel's skate.
Jones made it 2-0 at 19:07 off a Torey Krug turnover when his clearing attempt caromed off Ducks forward Ryan Getzlaf.
"Yeah, that's a tough play by me," Krug said. "I've got to make that, especially for our team. We were rolling there, so I'll take ownership on that.
"Just got to be better. If you want to be a player that's relied upon in big situations in this league, and especially on this team, a good team, you've got to step up when you're called upon, so I've got to make a better play there."
O'Reilly cut it to 2-1 at 10:50 of the third period when he scored from the slot on a delayed penalty with an extra skater on the ice. The Blues hadn't scored in 144:08, since a Vince Dunn goal at 6:42 of the second period in a 5-1 loss at the Vegas Golden Knights on Monday.
Grant's empty-net goal at 18:57 made it 3-1, and Rakell scored into an empty net at 19:55 for the 4-1 final.
"We did some good things," Steel said. "We stuck together and came up with two points. It was nice."
NOTES: Ducks defenseman Jamie Drysdale sustained an upper-body injury in the first period. There was no update postgame. ... This was Anaheim's first regulation win since Feb. 11. ... Blues forward Tyler Bozak had four shots playing 10:41 after missing three games with an upper-body injury. ... The Blues won six straight regular-season games against the Ducks dating to Jan. 13, 2020.