Beauchemin scored with 1:14 left in the third period, and the Avalanche edged the Devils 3-2 victory on Thursday night.
Nathan MacKinnon and Rene Bourque also scored for Colorado, and Calvin Pickard had 25 saves. The last-place Avalanche (19-44-3) will try for their first three-game win streak of the season on Saturday against Ottawa.
"We'll take the win," coach Jared Bednar said. "The guys were positive on the bench again and Beauch comes up with a big goal after a good shift from the (John) Mitchell line."
The Devils controlled the play for the last two periods, but Colorado caught a break when Beauchemin scored off his own rebound. He got his third goal of the season after New Jersey forward Devante Smith-Pelly missed with a poke check, opening up a shooting lane for the defenseman.
"We have a winger go out to the point, guy stick checks, (Beauchemin) swings by him, stays in, scores the goal," Devils coach John Hynes said. "Can't play like that with a 1:27 left. That's the game."
Beauchemin was happy to take advantage.
"It was a good feeling," he said. "Any win is great right now. It's a tough situation to be in, but we can try to get some positives by winning some games."
New Jersey trailed 1-0 before Hall scored his 15th of the season 42 seconds into the third. He began the day with eight goals in his last 11 games against Colorado.
Hall's goal ended a scoring drought of 174 minutes, 51 seconds that spanned four games. Ryan Spooner's goal 5:51 into the third period against Boston on Saturday was the last time New Jersey scored before Thursday.
"We have struggled to score goals at times this year and we're struggling right now," Hall said. "When that happens, you want to simplify things. As the game wore on, especially in the last two periods, we were getting that done."
The Avalanche answered 3:23 later when Bourque scored off a turnover in the Devils' zone. New Jersey tied it again at 6:13 when Noesen scored his fifth of the season.
MacKinnon went 15 games without a goal before getting an empty-netter against Carolina on Tuesday, and he made it two straight games with his 14th at 11:11 of the second.
New Jersey captain Andy Greene missed his fourth straight game, but did rejoin the team in Colorado. He left the team after the death of his father on Saturday.
Hynes said after the game that travel problems prevented Greene from meeting up with the team until Thursday, so he didn't play him.
"He didn't have a chance to skate; he hasn't skated since last Saturday," Hynes said. "If he got in (Wednesday) night he would have played but he had real tough travel coming in."
New Jersey C Jacob Josefson missed his fifth straight game with an upper-body injury. ... Colorado is now 1 for 27 on the power play over 12 games. The Avalanche were 29th in the NHL for power-play success at 13.5 percent coming into Thursday. Detroit is last at 12.6 percent.
Devils: At Arizona Coyotes on Saturday night.
Avalanche: Host Ottawa on Saturday night.
This version corrects to nine straight losses for New Jersey.