Oshie said the Blues have plenty to play for, even if that doesn't include chasing a playoff berth.
"Pride. Playing for the guys next to you," Oshie said. "Obviously, a huge part of it is playing for the fans that have supported us all year, even in our darkest hours when we weren't playing very good there. ... We'll play for them and from here on out and the guys sitting next to us."
The Blues won for just the second time in six games. They have 75 points and are 12 behind eighth-place Anaheim with eight games to play.
"It was a game that could have really gone either way in those first two periods," Blues coach Davis Payne said. "We didn't play our kind of hockey for the first two periods. Good thing we did in the third."
The Blues' three-goal third period sent the Oilers to their eighth consecutive loss, a stretch in which they've scored just seven goals. Edmonton's shots total matched a season low, and the Oilers didn't register a shot in the third period until there was 1:08 remaining in the game.
"It's real disappointing," defenseman Jim Vandermeer said of his injury-riddled team's performance. "But I think if we stick to the game plan by taking pucks to the net and get traffic there, it doesn't matter who we have in the lineup and who we play with and who we play against. To do that consistently, you're going to get opportunities."
Edmonton went 28:34 between shots in the second and third periods.
"It's frustrating, obviously," forward Jordan Eberle said. "We've got some guys out that help us with offense but collectively as a group, we should be able to put the puck in the net. I think it comes down to getting the puck to the net first off and getting second opportunities."
Oshie opened the scoring with 1:32 left in the second period by beating Nikolai Khabibulin to the short side with a wrist shot from the lower right circle.
"I figured he would be leaning," Oshie said. "Not a high-percentage shot, but it went in. I'll definitely take it."
D'Agostini made it 2-0 at 2:12 of the third period by snapping a shot from the lower left circle that squirted between Khabibulin's pads. Stewart, acquired from Colorado last month, added his 10th goal with the Blues and 23rd overall by finishing off Oshie's feed from the slot at 8:30.
Cracknell completed the scoring by one-timing a cross-ice feed from Kevin Shattenkirk past Khabibulin with 4:53 remaining.
"What we wanted to do, is keep the shot total down and limit their opportunities to feel good about their game," Oilers coach Tom Renney. "We did that until the start of the third period. They knew that we were here to play hockey.
"But the wheels didn't just wobble, they fell off. We needed a couple of kills that we didn't get and we needed to attack more and put more pucks on goal, play more hockey in their end. We had a hard time doing that eventually."
Material from team media and wire services was used in this report