In 1992 he earned the notice of the world hockey community as a member of the gold medal-winning Russian team at the World Junior Championships on a squad that included fellow NHL players Alexei Yashin, Darius Kasparitis, Alexei Zhitnik and Alexei Kozlov.
Before the World Juniors, he had been the San Jose Sharks' third choice in the 1991 NHL Entry Draft and the 30th pick overall while a member of Dynamo Riga in the Soviet league. After a stint with Kansas City in the IHL, he started with the Sharks in 1992-93.
But while Ozolinsh was a master at scoring and setting up goals as a result of his spectacular end-to-end rushes, he was also aware that he needed to develop a more complete game. The NHL opposition, after all, was quick to figure out a player's particular habits and patterns on the ice and could capitalize on an attacking defender's absence from the front of his own goal.
In October 1995, San Jose management traded Ozolinsh to Colorado for high-scoring winger Owen Nolan, a move that was met with great glee by Avalanche players and staff alike. Pierre Lacroix, the team's general manager, had big plans for the Latvian.
The trade paid big dividends for the Avs, who won the 1996 Stanley Cup with Ozolinsh firmly established as the team's power-play star and scoring defenceman. He was voted to the NHL First All-Star Team in 1997. After parts of five seasons in Colorado, Ozolinsh was dealt to the Carolina Hurricanes in the summer of 2000 where he played for parts of two seasons before joining the Florida Panthers midway through the 2001-02 season.
A member of Latvia's World Championship team and Olympic team in 2002, Ozolinsh remained with the Panthers midway through the 2002-03 season before he was acquired by the upstart Anaheim Might Ducks. Upon his arrival with the Ducks Ozolinsh played a key role helping the club reach the post season and their first Stanley Cup Final. Despite reaching their first Cup final, Ozolinsh and the Ducks were defeated in a hard-fought seven game series to the New Jersey Devils.
In 2003-04, the Ducks struggled and failed in their attempt in returning to the post season. Along with the Ducks struggles, their star defenceman battled injuries and was limited to a mere 36 games and following a lock out year in 2004-05, was dealt to the New York Rangers at the 2006 NHL trading deadline. He completed his 2005-06 as a Ranger and went on to miss the majority of the following season with a recurring knee injury.
In 2006, Ozolinsh represented his homeland in the 2006 Winter Olympics.