Kovalev scored for a fourth straight game 25 seconds in and Price made 28 saves to lead Montreal to a 4-1 win over the Chicago Blackhawks on Tuesday night.
"It was a pretty sad day for me when he got traded," Price said. "He was like an older brother to me."
Price and the Canadiens improved to 3-0-1 in their last four games.
"I think it was his best complete game in some time," said Montreal coach and GM Bob Gainey, who made Price the team's No. 1 goalie last season when he sent Huet to Washington at the trade deadline.
Kovalev, who assisted on Markov's power-play goal in the second, scored his 23rd goal when he beat Huet with Montreal's first shot as the Canadiens took advantage of Duncan Keith's blind back pass behind his net. He has scored five times during his streak.
"I think Dunc was expecting Kovalev to come on the other side, and just reversed the play. Kovy made a good read on it," said Huet, who stopped 29 shots in his first start in two weeks.
The Blackhawks goalie faced his former team for the first time since the Feb. 26, 2008, trade that sent him to the Capitals.
"He was always that guy that I could look up to," said Price, who went 24-12-3 last season as a 20-year-old rookie. "He was always there for advice, and if I was going through a rough time, he was there to help me out of it. He was everything I needed out of a partner and a veteran guy."
Sharp mustered the only offense for Chicago, which lost its second in a row following a 3-0-2 run that included a three-game winning streak.
The Blackhawks dropped to fifth overall in the West with 91 points, one behind fourth-place Calgary.
"If we play hard and we go out there and win games and fight as a team, the standings take care of itself," Chicago captain Jonathan Toews said. "Obviously, there are things we can't control. We had a tough loss against Vancouver the other night and now we don't play them again, so whatever happens away from where we are is out of our control. We've just got to focus on what we can do out there."
Canadiens forward Andrei Kostitsyn got 19 minutes in penalties 13:34 into the first for instigating a fight with Aaron Johnson. Kostitsyn had an unsportsmanlike conduct minor tacked on to his instigator, fighting major, and misconduct when he went after Johnson after the Chicago defenseman checked his brother, Sergei, into the boards behind the Blackhawks net.
"He saw his brother on the ice and his response was normal for the things that occur in the league," Gainey said.
Sergei Kostitsyn left the game with an upper body injury and didn't return. Montreal defenseman Roman Hamrlik also sustained an upper body injury in the second period that knocked him out of the game.
"I think [Wednesday] we'll have a better idea of whether they'll be practicing or traveling with the team," Gainey said.
Latendresse made it a 2-0 lead with his 13th goal 6:12 into the second period. Latendresse shot his own rebound off Huet and the puck flipped high in the air before sailing behind the Blackhawks goalie into the net.
Price kept his left pad stuck on the right post to deny Dave Bolland's deke attempt moments later.
Markov scored his 11th goal on a power play 15:52 into the second to increase Montreal's lead to three.
Sharp made it 3-1 when he spoiled Price's bid for his first shutout since Nov. 11.
Markov added an assist for his team-leading 62nd point on Schneider's power-play goal at 16:43.
The Canadiens, who are celebrating their 100th season, were originally scheduled to wear "barber pole" throwback jerseys honoring the 1912-13 team.
Previously worn during a 3-1 loss to Boston on Feb. 1, the sweaters and socks featuring narrow, horizontal bands of red, white and blue were set aside in favor of retro uniforms for the 1915-16 team that more closely resemble Montreal's current red jerseys.
- Huet, who debuted with Los Angeles, made his second career start against Montreal. Price faced the Blackhawks for the first time.
- Canadiens LW Alex Tanguay ended a five-game point streak. Tanguay had three goals and seven assists during the run, including the third five-point game of his career in a 6-3 win over Atlanta one week earlier.