Mikael Granlund had a goal and three assists, Carlsson and Jackson LaCombe each had a goal and an assist, and Lukas Dostal made 20 saves for Anaheim in its first home playoff game in eight years.
Connor McDavid had a goal and an assist, Leon Draisaitl and Evan Bouchard each had two assists, and Connor Ingram made 32 saves for the Oilers, who had leads of 1-0 and 3-2.
The Ducks have a 2-1 lead in the best-of-7 series. Game 4 will be at Honda Center on Sunday (9:30 p.m. ET; ESPN, SN, CBC, TVAS, Victory+).
The game was tied 3-3 entering the third period before Sennecke put the Ducks back in front, scoring far side from the left circle off a rush to make it 4-3 at 2:53.
Carlsson then converted a feed from Troy Terry on a 2-on-1 rush, deking to his backhand to tuck the puck in at the right post for a 5-3 lead at 3:35.
McDavid brought the Oilers back within a goal, getting Edmonton’s first power-play goal of the series with a wrist shot from low in the right circle that went off the stick blade of Ducks defenseman Pavel Mintyukov and off Dostal’s body to cut it to 5-4 at 8:36.
Jeffrey Viel controlled a loose puck at the end of an Anaheim rush and swept in a backhand from the bottom of the left circle to make it 6-4 at 16:57.
LaCombe scored into an empty net with 1:33 left for the 7-4 final.
Vasily Podkolzin scored with a snap shot from the right face-off circle to give the Oilers a 1-0 lead at 13:12 of the first period after Anaheim’s failed clear went right to his stick.
Ducks defenseman Drew Helleson took a shot from the right point that Mason McTavish tipped off the tip of Ingram's glove and into the net to tie it 1-1 at 16:18.
Granlund scored into an open net for a power-play goal, making it 2-1 Anaheim at 17:45 after Chris Kreider’s deflection of Carlsson’s shot went off Ingram’s pad and straight to Granlund.
After getting outshot 20-7 in the first period, the Oilers scored twice in the first six minutes of the second period to move back in front.
Kasperi Kapanen scored his third goal of the series with a snap shot from the right circle to tie it 2-2 at 3:57.
Dostal couldn't cover the puck after making a save on Bouchard and Ryan Nugent-Hopkins jammed it into the net for a 3-2 lead at 5:39.
The Ducks tied it 3-3 at 12:37 when Granlund got to a rebound in the slot area and pushed it to Alex Killorn at the bottom of the left circle for a shot into the open side of the net.
