Then with 3:24 remaining in the first period, Olofsson did what he does best: score on the power play.
With Jeff Skinner poking around the front of the net, the puck eventually made its way to Sam Reinhart, who was able to find Olofsson locked and loaded for a one-timer in front.
Olofsson's quick release extended the NHL record he set last game. He is now the only player in league history to score his first eight career goals on the power play. He scored twice while on the man advantage last year and has six power-play goals so far in 2018-19.
The Sabres put the pressure on early, but Anaheim eventually fought back against that early Buffalo pressure and generated some high-danger chances of their own late in the period. They were finally able to capitalize with 1:53 remaining when Max Jones scored, but the goal was called back when Buffalo won an offside challenge.
So what did Anaheim do? They came right back and scored again. This one, a deflection in front by Henrique, counted and cut Buffalo's lead to one heading into the second period.
Anaheim tied it 57 seconds into the second when Jakob Silfverberg picked off a puck in the corner and fed Rickard Rakell in front to make it 2-2.
Ryan Getzlaf scored on the power play 9:14 into the middle frame to give the Ducks the lead. Then Henrique beat Ullmark again with just 12.5 seconds remaining in the period.
Henrique now has 22 points (8+14) in 24 career games against Buffalo.
Silfverberg added an empty netter with 3:13 left in regulation.