Martin Brodeur made an outstanding left pad stop on Samuel Pahlsson's shot from the doorstep, but the rebound came out to the edge of the right faceoff circle, where Thomas, a former Devil, put the puck under the goaltender's glove.
The third-quickest overtime goal in Stanley Cup Finals history boosted Anaheim to 7-0 in overtime in the postseason and a remarkable 12-1 in one-goal decisions.
Jean-Sebastien Giguere made 26 saves for his fifth playoff blanking, extending his playoff-record overtime shutout streak to 168 minutes, 27 seconds.
Brodeur stopped 25 shots but could not prevent the Devils from suffering consecutive losses for the second time in this year's playoffs.
Game Five is Thursday in New Jersey, where the Devils are 10-1 in the postseason. The Ducks raised their home record to 8-1.
There were few scoring chances in a cautious third period. One of the best came with 15:33 remaining when a dump-in by Game Three hero Ruslan Salei took an awkward bounce off the right boards and slid toward Brodeur.
Beaten by a carom in Saturday's loss, Brodeur had the puck go off his glove but gathered it with his stick just before it could cross the goal line.
Less than four minutes later, Brodeur denied Mike Leclerc on a quick shot from the bottom of the left circle.
Things opened up after the fourth straight scoreless opening period in the series.
Rookie Stanislav Chistov tested Brodeur with a wrist shot from the slot, but New Jersey's Patrik Elias won a faceoff less than a minute later and flicked a shot off the left goalpost.
Three minutes later, Chistov's wrister from the high slot hit the right elbow where the post and crossbar meet.
The Devils nearly grabbed the lead on their third power play, but Giguere squeezed his pads to stop Brian Gionta's redirection of Sergei Brylin's pass off the left side with just under 10 minutes to go.
Giguere stopped another deflection with 2:46 left, smothering John Madden's tip of defenseman Scott Niedermayer's one-timer from just inside the blue line.
Madden broke in alone on the left side, but Giguere caught his slap shot in his chest just before the final buzzer.
As they did in Game Three, the Devils wasted two power-play chances in a scoreless first period.