Bishop made 17 saves after replacing Lehtonen early in the second period with Edmonton leading 3-2.
Caggiula scored his second goal of the game less than one minute into the second.
Cam Talbot made 15 saves for the Oilers.
The Stars didn't have a shot on goal until Roussel scored at 6:36. Two minutes later, Radulov took a pass from Roussel high in the right faceoff circle and sent a slap shot into the lower right corner of the net.
Edmonton tied the game at 2 on a short-handed goal by Caggiula and a power-play score by McDavid 52 seconds apart.
The Oilers took the lead when Caggiula put in the rebound of a shot by Darnell Nurse. Bishop then replaced Lehtonen, who made 10 saves in 13 shots.
With a goal and an assist, Benn has 29 points (17 goals, 12 assists) in 27 career games against Edmonton. ... McDavid has seven goals in six games vs. Dallas. ... Stars D Marc Methot (lower-body injury) missed his fifth straight game. ... The first period ended with a fight along the boards. Oleksiak and Edmonton's Patrick Maroon received major penalties. Roussel and the Oilers' Matt Benning each had a minor and misconduct penalty. ... Dallas has allowed power-play goals in seven of the last nine games.
Oilers: Play the second game on a five-game trip Tuesday at St. Louis. The Blues won 4-1 at Edmonton on Thursday.
Stars: Host Montreal on Tuesday in the second of two home games.