The win was the 27-year-old rookie goaltender's 20th since the Senators recalled him from their American Hockey League affiliate.
Hammond finishes the regular season with a 10-0-2 record on the road.
Mark Stone, a candidate for NHL rookie of the year honours, scored the game's opening goal at 6:06 of the first period and completed the scoring with his 26th goal of the season in the third.
Jean-Gabriel Pageau had the other goal for Ottawa, which looked be a playoff longshot a few weeks ago until it started a 22-4-4 run.
The Senators' win means either Tuukka Rask and the Boston Bruins or Sidney Crosby and the Pittsburgh Penguins will have their playoff hopes dashed Saturday evening.
More to come