Sean Monahan scored and Chad Johnson made 20 saves for the Flames, who were eliminated by the Ducks in their previous appearance in the Stanley Cup Playoffs in five games (Western Conference Second Round, 2015).
"It [stinks]," Monahan said. "Getting into the playoffs, it's the most fun to play hockey in the playoffs, and you go out in four [games]. It's not a good feeling. We've got a good team here and we've got to get ready to go for next year.
"Right now and throughout the summer, getting swept in four is going to sting. But coming back next year, this is an exciting team to be on."
Eaves scored on Flames starting goalie Brian Elliott from a sharp angle along the boards just below the hashmarks on the Ducks' third shot of the game to take a 1-0 lead 5:38 into the first period. The goal prompted Flames coach Glen Gulutzan to pull Elliott for Johnson.
Elliott, who finished with two saves, allowed five goals on 27 shots in Game 3 and entered Game 4 with a 3.67 goals-against average and .887 save percentage in three playoff starts.