Ozoliņš joined the Sharks in 1992–93, scoring 23 points in 37 games. He missed the majority of his rookie season recovering from a knee injury suffered in a game against Philadelphia on December 30, 1992. After recovering from his injury, Ozoliņš ended the 1993–94 season with an 81-game, 26-goal/64-point sophomore effort, leading the league in goals by a defenceman. Ozoliņš helped the Sharks to move beyond the first round of the playoffs for the first time in franchise history, losing in the conference semifinals.