The Mighty Ducks earned two pivotal points with the victory over their division rivals.
Oates opened the scoring 61 seconds into the first and set up a power-play goal by Petr Sykora which gave the Mighty Ducks a 3-1 lead with 2:57 left in the period.
Anaheim took a 3-2 advantage into the first intermission, and scored the decisive goal 2:27 into the second period when Steve Rucchin found the net on a power play.
Sykora and defenseman Niclas Havelid each had a pair of assists for the Ducks, who built an eight-point lead over San Jose and Phoenix for second place in the Pacific Division, and held on to eighth in the Western Conference.
Owen Nolan scored twice to stretch his goal-scoring streak to six games, but the Sharks had a three-game winning streak snapped. They had won the first two meetings between the teams this season.