Reaves scored his second goal at 2:58 of the second period to cut it to 3-2.
Strome credited Reaves and linemates Kevin Rooney and Greg McKegg for sparking the Rangers after a difficult first period.
"Even without the goals, I think the whole game they were the only line that was able to get in there and forecheck and create turnovers and have sustained zone time," Strome said. "We fed off that. They provided energy the whole night."
Fox tied it 3-3 at 17:49 when Strome passed to him cutting through the right circle for a one-timer through Campbell's legs.
"We took our foot off the gas, and it's becoming something we really need to stop doing and fix," Marner said. "This isn't something we were doing at the start of the year."
Shesterkin kept the game tied when he made a glove save on a breakaway by William Nylander at 2:11 of the third period. He saved the final 27 shots he faced after giving up three goals on 11 shots in the first.
"It shows our maturity," Reaves said of the comeback. "It shows that we can hang with the big boys, that we are one of the big boys."
NOTES: Matthews failed to tie the record 11-game road goal streak held by Pavel Bure (1993-94 with the Vancouver Canucks) and Steve Yzerman (1988-89 with the Detroit Red Wings). … Since Marner last scored a power-play goal, 426 NHL players scored at least one, led by Edmonton Oilers forward Leon Draisaitl (34). Among the Maple Leafs, 15 players scored at least one, including 22 by Matthews. Marner had 28 power-play assists in that span. … New York is 11-2-0 against the Atlantic Division and 17-3-0 against the Eastern Conference. … Kreider's goal was his 25th of the season, which tied Matthews for third in the NHL, behind Draisaitl (26) and Washington Capitals forward Alex Ovechkin (27). … Rangers forward Mika Zibanejad had two assists to extend his point streak to six games (three goals, four assists).