Jonathan Marchessault also scored for the Golden Knights, and Robin Lehner made 39 saves.
Brady Tkachuk scored the lone goal for Ottawa, and Anton Forsberg made 40 saves.
Vegas entered the game with the worst power play in the NHL since Jan. 24 at a bleak 5.4 per cent (2 for 37) conversion rate, and was already 0 for 1 in the game.
Ottawa’s Thomas Chabot was called for tripping with 54 seconds left, giving the Golden Knights their second power-play opportunity. Eichel, Vegas’ newest $10 million dollar man, sent the crowd into a frenzy by scoring after the puck caromed to him on the left side and he fired it past Forsberg for his third score of the season.
While Eichel was credited with the winner, Lehner may have had the play of the night early in the third period. Nick Paul strolled in from the corner and fed Zach Sanford in front of the crease, but Lehner stopped the chance with a spectacular glove save.
After a scoreless, albeit lively, first period in which the Golden Knights outshot Ottawa 17-15 and held an edge in scoring chances (13-8) and high-danger chances (4-3), both teams got on the board in the second.
Marchessault raced in untouched from Vegas’ zone and through the slot and sent a wrist shot high over Forsberg’s glove. Marchessault extended his point streak to five games with four goals and two assists in the span.
The lead didn’t last. Ottawa’s power play, which had struggled on the road, scored the equalizer after Vegas’ Michael Amadio was called for tripping. The Senators methodically worked the puck to the goal line, where Colin White was in the right spot to feed Tkachuk for a tap past Lehner.
The Senators came into the game with the second-worst road power play in the NHL, having converted just 13.2 per cent (10 of 76) of their opportunities before their first chance Sunday.
Senators: Conclude a five-game road in St. Louis on Tuesday.
Golden Knights: Open a five-game trip in Philadelphia on Tuesday.