Howard has won his past two starts after a five-game losing streak (0-5-0). Dylan Larkin and Frans Nielsen scored for Detroit, which led 2-0 entering the third period.
The Red Wings had blown three-goal leads in the third period their past two games, a 5-4 overtime win at the Washington Capitals on Sunday and a 7-6 overtime loss at the New York Islanders on Friday.
[WATCH: All Ducks vs. Red Wings highlights]
"We were happy with a two-goal lead," Red Wings captain Henrik Zetterberg joked. "We didn't want another three-goal lead."
Detroit (23-23-9) is eight points behind the Carolina Hurricanes for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"We know our situation and what has to be done," Larkin said. "We're desperate right now."
The Red Wings went 4 for 4 on the penalty kill after allowing six power-play goals in their past two games.
"I thought our kill was really good tonight," Detroit coach Jeff Blashill said. "We got tested tonight, and we had a great response."
Video: ANA@DET: Howard makes a big save on Perry in front
Anaheim (27-20-11), which has lost two straight games (0-1-1) and five of seven (2-3-2), is tied with the Los Angeles Kings for fourth place in the Pacific Division, one point behind the third-place Calgary Flames. The Ducks trail the Minnesota Wild by three points for the second wild card from the Western Conference.
"The last week or so has been frustrating, because we're not competing at the level that we're capable," Ducks center Ryan Getzlaf said. "We have to push for the playoffs right now. We don't have time to wait."
The Flames lost 5-2 at the Boston Bruins on Tuesday, and the Kings lost 7-3 at the Hurricanes.
"We can't look at this as any kind of moral victory, just because other teams lost a game," Ducks coach Randy Carlyle said. "This was a great opportunity for us to make up some ground, and we didn't take it."
Adam Henrique scored, and John Gibson made 14 saves for Anaheim.
Video: ANA@DET: Henrique crashes net to pot rebound in 3rd
The Ducks nearly took a 1-0 lead at 9:32 of the first period when Jakob Silfverberg hit the post from the edge of the crease with Howard out of position. The Red Wings knocked the rebound into their own net, but the referees ruled the whistle had blown.
Larkin made it 1-0 at 13:32 of the first, intercepting Kevin Bieksa's pass in front of the net and beating Gibson with a backhand for his ninth goal of the season.
"That was a nice surprise," Larkin said. "I just had had my stick out and the puck hit it."
Anaheim put the puck in the net at 1:33 of the second period, but the goal was disallowed because of goaltender interference on Nick Ritchie.
"We played well early in the game, but we had two goals called back on close calls … and they get one on the turnover," Getzlaf said. "I think that took something out of us."
Nielsen made it 2-0 with 4:23 remaining in the second period, one-timing Anthony Mantha's pass through traffic for his 13th goal. Nielsen has seven points (two goals, five assists) in a five-game point streak.
"I'm having a bit of luck right now," Nielsen said. "You go out there and work hard every night, and sometimes things bounce your way."
After Nielsen hit the crossbar on a breakaway with 4:45 remaining in the third period, Bieksa's shot hit Howard's shoulder, rolled down his back and was tapped in by Henrique to make it 2-1 with 3:54 remaining. It was Henrique's 17th of the season.
"I made the move I wanted and got the puck up, and I just hit the bar," Nielsen said. "When they went right down and scored, I was thinking 'Is it going to be one of those again?' but we did a good job at the end."
Goal of the game
Nielsen's goal at 15:37 of the second period.
Video: ANA@DET: Nielsen buries Mantha's pretty no-look feed
Save of the game
Howard's save on Henrique at 9:46 of the first period.
Video: ANA@DET: Howard stops Henrique, stones rebound chance
Highlight of the game
Larkin's goal at 13:32 of the first period.
Video: ANA@DET: Larkin steals puck, finishes with backhand
They said it
"The puck was bouncing on us, but we needed to get more shots up on [Howard]. We were putting too many shots into his feet, and that doesn't give us the kind of rebounds we needed." -- Ducks coach Randy Carlyle
"This was close to a playoff game, because both teams needed it, so there wasn't a lot of room out there. It was fun to play a game like that, and we found a way to grind out a win." -- Red Wings captain Henrik Zetterberg
Need to know
Bieksa's assist was his first point in 18 games since a 5-2 win against the Arizona Coyotes on Dec. 31.
Ducks: At the Chicago Blackhawks on Friday (8:30 p.m. ET; NBCSCH, PRIME, NHL.TV)
Red Wings: At the Tampa Bay Lightning on Friday (7:30 p.m. ET; FS-D, SUN, NHL.TV)
Video: Larkin, Howard lead Red Wings to 2-1 win vs. Ducks