Vatrano has now scored in three of his last four games and is third among team leaders in goals this season.
With a pair of first-period helpers, his team-leading 17th and 18th points of the season, Terry pushed his scoring streak to four games.
Ottawa would briefly pull even with a power-play tally of their own moments later, a tip by Tkachuk parked right in front of Dostal amidst a 5-on-3 advantage.
With an assist, Ottawa's Tim Stutzle became the fastest Sens skater to record 30 points in a season since Matt Duchene in 2018-19. Stutzle leads the Senators in points and assists, and ranks third in goals.
The goal snapped a streak of 15 successful penalty kills by the Ducks.
Anaheim would respond before the end of the period though, executing a last-second rush up ice with several on target cross-ice passes - eventually leading to LaCombe crashing the net and punching home a rebound over the sprawled Ullmark's left leg pad.