Schneider also appeared to survive an injury scare with about 10 minutes left in the third when Tampa Bay defenseman Ryan McDonagh collided with him.
Alex Killorn and Steven Stamkos each had a power-play goal and an assist for the Lightning.
"Hall is not happy that he's playing his first playoff game, or third playoff game, the guy just wants to win", Devils coach John Hynes said.
Hall was the Devils MVP during their stunning run from the worst team in the Eastern Conference to the postseason in a year, and he didnt disappoint in their biggest game of the season.
Pavel Zacha blocks Tyler Johnson's shot.
Butcher tied the game after the Lightning were whistled for too many men on the ice. To their credit, the Devils held on for 5-2 and 5-3 losses on the road, but they'll have a chance to tie it all up when they return for two home games. Kucherov sent a pass from behind the goal line that Killorn redirected into the net before Schneider could move.
Hall tied it 1-1 at 12:24, beating Vasilevskiy five-hole with a slap shot from the slot. He then whipped a pass to Noesen, who one-timed the shot from the right circle past Vasilevskiy. He hit the crossbar on a first-period breakaway.
The Devils took their first lead of the series when Hall skated through the neutral zone and flew by J.T. Miller before stopping in the left circle.
Lightning vs. Devils Live Stream: Watch NHL Playoffs Game 3 Online
Schneider's save on Tyler Johnson at 9:50 of the third period.
C Cory Conacher will replace Callahan on the fourth line with Cedric Paquette and Chris Kunitz. Michael Grabner, who was acquired in mid-February from the Rangers, is not in the lineup. Mirco Mueller also sat as New Jersey dressed six defensemen instead of seven used in Game 2.
Monday night's game will mark the return of forward Marcus Johansson to the lineup.
"We know what we did in Game 1 and 2 is not good enough", Cooper said. Frederik Andersen stopped 40 shots. Hall has five points (two goals, three assists) in the series. Game 4 is here Wednesday. Game 3 is Monday, while Game 4 is Thursday back in Toronto. Tampa Bay was 2-for-5. "We have to raise our game again to get the results we need here or it's going to be a tough one". They lost the leads and eventually the contests in overtime, twice, and are now headed to Columbus for Game 3 and Game 4.
An Andy Greene slashing penalty in the closing seconds of the first period led to a Lightning power play to start the second period.
But the Bruins again responded when Chara ripped a shot off Andersens mask and in from an impossible angle at 6:19. Hall's took a drop pass from Brian Boyle and wristed a shot under the left arm of Lightning goalie Andrei Vasilevskiy for his second goal of the series.
The Maple Leafs had a number of chances early as they returned to a boisterous Air Canada Centre before a controversial sequence led to the opening goal. You never know. We have skill to put the pucks in as well.
Blake Coleman raced to a puck along the boards in front of the Devils' bench and chipped a long shot into an empty net with 57.3 seconds to play for a 4-2 lead, and Ben Lovejoy added another empty netter with 38 seconds left.
Wanted: A US strategy on Syria
The mechanism would look at cases where the OPCW fact-finding mission has established chemical weapons were used or likely used. The move was part of a joint Russian-US deal that averted military action threatened by the then US president, Barack Obama.
Alberta proposes bill to control oil, gas exports
But she said Alberta is "very committed to putting pressure on B.C.to come around and focus on what this pipeline actually means". An expansion to the West Coast has been approved by the federal government, but B.C.is fighting it in the courts.