In 1989, at the age of 16, Kovalev was included on the first string of a top-rated Soviet club, Dynamo Moscow. In that year, the mass exodus of Soviet hockey players hadn't yet begun. Even though he stood out among his teammates for his superb skating and original stickhandling technique, Kovalev didn't call the shots.
In the Dynamo Moscow lineup, Kovalev flew across the Atlantic to participate in a number of exhibition games a year later. As Yurzinov admitted later, he took Kovalev on that tour in order to give him a chance to see the best of modern hockey with his own eyes and to size up his future opponents. But Kovalev wanted to play and became offended if the coach failed to include him on the playing list for a game.
At first, the eminent coach Mike Keenan, followed by his pupil and successor in the post of New York Rangers head coach, Colin Campbell tried to restrain Kovalev's individualistic impulses while on the ice and get the young player to play strictly according to his position. But sticking to his guns and remaining true to his style of play was nothing new to Kovalev.
Kovalev was grateful to Yurzinov for his lessons in game strategy and for the limited amount of freedom the coach did allow him within the constraints of the play. To his credit, Kovalev withstood the pressure from his coaches and didn't change his style. Just over a year later, he was playing such a stylish game of hockey that he attracted attention and was offered his first serious position. Keenan actually placed Kovalev on the first forward line with the team's top offensive talent. The Kovalev-Mark Messier-Adam Graves line determined the outcome of the battle for the Stanley Cup in the spring of 1994. To top it off, Messier became a top scorer in the league during the playoffs.
With Keenan, one of the toughest coaches in the NHL, Kovalev was able to accomplish that. Many Europeans in the NHL had trouble adjusting to the different style of play after being pressured to give up their own style. Just a little over 20, Kovalev, with his fighting spirit and winning style, had conquered New York. With his peculiar stickhandling and masterly skating, his ability to set up his partners in scoring positions and his powerful shots on goal, he garnered a lot of attention in his new homeland. Over the years, fans began showing up for games in Madison Square Garden wearing hockey jerseys with the number 27 and Kovalev's name stamped on the back.
With the Pittsburgh Penguins, which he joined in 1998, Kovalev was allowed to continue his own style of play and immediately became one of the leaders of the team. "Kovy" as he is known to his teammates spent parts of five seasons with the Penguins, where he established a career high 95 points in 2000-01.
A two-time Olympic medalist, gold in 1992 with Team Unified and bronze in 2002 with Russia, Kovalev headed back to the Big Apple towards the end of the 2002-03 season. After the Penguins felt they would be unable re-sign the talented forward during the off-season, they traded him back to the team whith whom he began his career with, the New York Rangers.
In 2003-04, the Rangers struggled and saw that their playoff hopes were vanishing, and as the season progressed they opted to trade the talented forward to the Montreal Canadiens for young prospect Josef Balej and a second round pick in the 2004 NHL Entry Draft. In 2006, Kovalev would represent Russia in the 2006 Winter Olmypics.
In his second season in Montreal, Kovalev struggled to produce offensively and at times was heavily criticized by local media and fans alike. However, he rebounded during the 2007-08 season. Matched with Andrei Kostitsyn and Tomas Plekanec, he tallied a total of 35 goals and 49 assists for a total of 84 points in 82 games. He was called by many the comeback player of the year for his amazing turnaround season, as the Canadiens captured top seed in the Eastern Conference.
The summer of 2009 saw Kovalev become an unrestricted free agent and with the Canadiens apparently headed in another direction, Alex found himself in search of employment. He wouldn't be out of work long and wouldn't have to travel far to find his new home. With change also occurring in the nation's capital, a spot became available on the Senators top two lines and the two sides reached a deal that would see Kovalev suit up for Ottawa.
Kovalev's time in the nation's capital was not as offensively productive as he and the team would have liked, though he did reach a personal milestone while wearing a Senators jersey. On November 22, 2010, Kovalev recorded his 1,000th career point in a game against the Los Angeles Kings.
On February 24, 2011, Kovalev's time in Ottawa would come to an end. He was traded to a familiar destination, the Pittsbugh Penguins in exchange for a conditional draft pick.