The victory was the first for the Oilers in four games, which included a 3-0 loss to the Blues on Saturday in Edmonton. It was the Oilers' first win in St. Louis since Dec. 11, 2009.
Despite notching a season high in shots, St. Louis lost for the third time in four games and was shut out for the third time this season. It also had a four-game home winning streak snapped.
Taylor Hall, who assisted on both of Eberle's goals, also scored. It was his eighth of the season off a rebound from Eberle, who skated in on a breakaway.
Khabibulin earned his first shutout of the season, and the 46th of his career.
He stopped 21 shots in the second period, including two breakaways. He first kept David Perron from scoring to set up Eberle's second goal and later stopped David Backes from close range.
Eberle has nine goals this season and his three-point night ended a three-game drought. It also marked his first three-point game of the season. It's the second time he has scored twice for the Oilers. He notched two goals in a 6-4 victory over Colorado on Feb. 16.
Jake Allen entered the game with an 8-2 record and 2.26 goals-against average, before giving up three goals on seven shots. He was pulled after Hall's goal and replaced by Jaroslav Halak.
The Oilers finished with 19 shots.
NOTES: The Blues have been shut out three times this season. ... Hall's two assists were his first in four games, after getting five in a four-game span. ... Edmonton has outscored its opponents 28-22 in the first period this season. ... This was the third and final game between the teams this season with all games played in March. ... Ladislav Smid entered the game leading the league in blocked shots with 89.Suggest a correction