Laviolette didn't provide an update on the severity of the lower-body injury Vanecek sustained while failing to stop Jake DeBrusk's goal that tied the game 1-1 with 6:50 remaining in the first period.
The 25-year-old rookie was making his Stanley Cup Playoff debut after leading NHL rookies in wins (21-10-4) with a 2.69 goals-against average, .908 save percentage and two shutouts during the regular season.
Vanecek's injury pushed Anderson into his first NHL playoff game since May 25, 2017, for the Ottawa Senators in Game 7 of the Eastern Conference Final, a 3-2 double-overtime loss to the Pittsburgh Penguins. Anderson, who turns 40 on May 21, spent most of this season on Washington's taxi squad and played four games, including two starts.
Anderson allowed one goal on 22 shots, holding the Capitals in the tight-checking game until Nic Dowd scored the winning goal 4:41 into overtime.
"In this time of year, it doesn't matter what happened," Washington captain Alex Ovechkin said. "Somebody gets hurt, somebody didn't have a game right, we have to find a way. I think everybody understands that. It is time for us to step up."
Anderson was the backup because Ilya Samsonov was not available after being removed from NHL COVID-19 protcol Saturday afternoon. Samsonov hasn't played since May 1, when he made 23 saves in a 3-0 loss to the Pittsburgh Penguins.
Samsonov and center Evgeny Kuznetsov were scratched for disciplinary reasons for a 6-3 win against the New York Rangers on May 3 and entered COVID-19 protocol the next day.
Samsonov, along with Kuznetsov, was on the ice for an optional practice Sunday, but how much time he'll need before he's ready to play is unknown. He was 13-4-1 with a 2.69 GAA, .902 save percentage and two shutouts this season.
That leaves Anderson as the likeliest candidate to start Game 2. He was 2-1-0 with a 2.13 GAA and .915 save percentage in the regular season. He made 28 saves in a 2-1 overtime win against the Philadelphia Flyers on May 8, his first start since Feb. 22.
"Well, you could say I'm well-rested from not playing so much," Anderson said jokingly. "I think it's one of those things coming into the year, I knew the situation, I knew the role that I was asked to do. I think opportunity knocks, you make the most of your opportunity."