Nick Jensen had a goal and an assist as the Senators won for the fourth time in five games. Nick Cousins and Michael Amadio both had two assists.
Ullmark got his second shutout of the season and 10th of his career.
Pyotr Kochetkov made 19 saves, but the Hurricanes were shut out for the second time in six games and lost for the fifth time in the last seven.
Pinto converted from the slot off a short pass from Amadio at 4:04 of the second period to open the scoring. Pinto added an empty-net goal with 47 seconds left.
The Senators beat the Hurricanes for only the sixth time in the last 20 meetings, with the first road win in the season in more than three years.
Senators: Ottawa’s best groove of the season is largely connected to the defensive end. The Senators haven’t allowed more than one goal in any of their past four victories.
Hurricanes: Carolina has trailed at some point for the 11th straight game.
The Hurricanes threatened a few times in the second period, with Ullmark deflecting Brent Burns’ shot off his mask to maintain the 1-0 lead.
The Senators killed off two Carolina power plays in the first period, so now they have gone 7-for-7 on penalty kills over the past two games. That’s a good boost for a team ranked 24th in the NHL in penalty-killing.
Senators host Pittsburgh on Saturday, while Hurricanes host Columbus on Sunday.
