Jackson Blake also scored for the Hurricanes, who are the No. 1 seed from the Metropolitan Division and Eastern Conference. Frederik Anderson made 21 saves.
Drake Batherson scored for the Senators, who are the second wild card from the Eastern Conference. Linus Ullmark made 25 saves.
Jake Sanderson, Ottawa’s top defenseman, left the game in the second period. He was hit in the head by Hurricanes forward Taylor Hall at 4:24 of the second period. Hall was assessed a minor penalty for an illegal check on the play. Sanderson played two shifts after the hit by Hall. He also appeared to hurt his hand blocking a shot before heading down the tunnel.
Carolina will go for the sweep of the best-of-7 series in Game 4 here on Saturday (3 p.m. ET; TVAS, SN, TBS, truTV, FDSNSO, HBO MAX).
Stankoven became the first player in franchise history to score the opening goal in three straight Stanley Cup Playoff games at 5:13 of the first period for the 1-0 lead. Hall picked up his own rebound off Ullmark, skated around the net and found Stankoven in the left face-off circle, where the forward one-timed it bar down over the blocker of Ullmark.
Batherson tied the game 1-1 at 16:06 of the second period. Nick Cousins found Batherson down low alone, who went forehand-backhand over the pads of Anderson.
Just 1:23 later, Blake gave the Hurricanes the lead, 2-1, at 17:29. K’Andre Miller sent a cross-ice feed to Blake, who sent a wrist shot past a sprawling Ullmark.