Matt Duchene also scored in the shootout for the Avalanche, who have won three straight - with the last two thanks in large part to the play of their reticent goaltender.
''I hate talking about myself. Ask Patrick,'' Varlamov said, deferring to coach Patrick Roy.
Colorado didn't need much offense with Varlamov in net. After stopping 46 shots in a 3-2 overtime win in Chicago on Tuesday, Varlamov had another strong game against the Devils. He made five saves on a power play early in the third and then made another on Patrik Elias' point-blank shot from the slot with about 13 minutes left.
The Avalanche nearly took a 2-0 lead on Duchene's wrister moments later, but Schneider made the save.
Varlamov had five saves in overtime and then stoned Elias and Adam Henrique in the shootout.
''I got a guy lying on his stomach and I couldn't finish it,'' Elias said.
Roy had no problem praising his goalie.
''I like the effort we had from our goalie. He made some great saves,'' Roy said. ''We put a lot on our goalie and our goalie has been phenomenal.''
The Devils are 0-8 in shootouts this season, with Schneider losing half of those. New Jersey has lost 12 straight shootouts dating to last season.
Schneider couldn't end the drought after keeping his team in the game for the first two periods.
''I don't know what it is right now, I'm not coming up with the saves in the shootout,'' he said after his fourth shootout loss of the season. ''When you're not getting wins from it and you're leaving points on the table, it matters.''
The Avalanche played without center Paul Stastny (leg) and defenseman Cory Sarich (back) for the second straight game. Roy chose to dress just 11 forwards and go with seven defensemen against the Devils.
O'Reilly, double-shifting on the fourth line, opened the scoring at 8:55 of the first. He took a pass from behind the net from Patrick Bordeleau and beat Schneider with a high snap shot from the slot. It was his team-leading 18th of the season.
''We ran a cycle play after Malone kept the puck in,'' O'Reilly said. ''Malone did that and Bordy saw me alone out front and I got the shot off quick.''
Colorado held a 13-2 shot advantage in the second period and controlled play for most of the first 40 minutes. Things changed in the third when New Jersey found its legs and put 18 shots on Varlamov.
''The way we played in the third, it seemed like they couldn't play with us,'' Elias said. ''It was like two different games.''
The Devils tied it at 1 when Loktionov beat Varlamov with a slap shot from the right circle at 8:59.
New Jersey's Steve Bernier nearly scored right after that when his shot skipped through the crease.
NOTES: Duchene celebrated his 23rd birthday Thursday. ... The Devils activated Elias and C Jacob Josefson from IR and assigned F Mike Sislo to Albany of the AHL ... Colorado sent G Sami Aittokallio to Lake Erie of the AHL. Aittokallio served as Varlamov's backup while Jean-Sebastien Giguere dealt with back spasms.