Liljegren also scored, William Nylander had an assist for his 400th NHL point, and Ilya Samsonov made 27 saves for the Maple Leafs (30-11-8), who are 2-0-0 thus far on their season-high five-game homestand, including a 5-2 win against the New York Islanders on Monday.
"It was a nice game, a great battle with [Shesterkin]," Samsonov said. "It was a little bit bigger game for me than normal against Shesterkin, Ilya Sorokin (Islanders) and Connor Hellebuyck (Winnipeg Jets, 4-1 win Jan. 19) too. Three good goalies. I'm happy we won; [it was a] hard game. Mitch [did] an excellent job in overtime, so [it's] nice."
Filip Chytil scored twice, and Shesterkin made 32 saves for the Rangers (26-14-8), who are 3-0-3 in their past six road games.
"They're a really good team," New York coach Gerard Gallant said. "They're really talented and when they're losing they're going to push, so they made a good play and they attacked and they got a goal. But no, I liked the game. I thought we played well in a tough building with a real good team against us. … I want the two points, but we'll take the one and run."
Liljegren tied it 2-2 at 15:49 of the third period, scoring glove side on a rebound from edge of the right face-off circle after getting the inside position on Rangers forward Chris Kreider.
"I think I feel a little bit more comfortable going down [in the zone] now," said Liljegren, a defenseman. "Especially that time in the game, we were down one goal and needed a goal, so try to get some more offense. In that period of time, if it's 2-2 maybe stay back a little bit, but I feel more confident in those areas."