Pearson scored on the rebound of a J.T. Miller shot on a power play at 9:48 to put the Canucks ahead 4-3, and then made it 5-3 on a long shot under Rittich's left pad at 13:36.
"I don't know what happened in the third," said Rittich, who is 0-1-1 since being acquired in a trade from the Calgary Flames on April 11. "I have to figure it out."
Sutter scored his second goal shorthanded into an empty net with 36 seconds left for the 6-3 final.
"A lot of people were thinking that we couldn't win either one of these games, and our team is here to win," Canucks coach Travis Green said.
Toronto is in first place in the seven-team Scotia North Division, four points ahead of the Winnipeg Jets. Vancouver is sixth, eight points behind the fourth-place Montreal Canadiens with four games in hand. The top four teams will qualify for the Stanley Cup Playoffs.
"In order for us to have a chance we just have to approach every game as a must-win," Holtby said. ""This shows that we're not out of it. I think we're kidding ourselves if we think two games is going to be enough. These two games we needed to win them in order to stay in it and now it's get back to work, keep pushing if we want an honest chance of competing down the stretch."
Tavares put Toronto ahead 1-0 at 16:55 of the first period on a play created by William Nylander, who was questionable to play after being late for a team meeting and being held out of his usual role in practice Monday. Nylander, who had two assists, said he missed a text message about the meeting.
Sutter tied it 1-1 at 5:33 of the second period when he scored on a rebound, and Hughes put the Canucks ahead 2-1 at 10:08 with a shot from the top of the left circle that deflected off Mitchell Marner's stick over Rittich's glove.