Brodeur made 37 saves Saturday night in the Devils' 3-2 win over the Ottawa Senators, but it was the two-goal performance by Asham that was the difference maker.
"Ash has responded," Devils coach Brent Sutter said. "If he's finishing and getting involved it gives him opportunities to get the puck to shoot. He's got a great shot and he hasn't shot the puck enough. Sometimes he gets cute and tries to make the perfect play and gets off track. He just needs to go hard up and down his wing."
Zach Parise scored the other goal for the Devils (33-21-5), who are just two points behind the Senators for first place in the Eastern Conference. Brodeur collected his 31st win of the season.
The Senators (34-20-5) fell behind 3-0 midway through the game but got a second-period goal from Jason Spezza and one from Chris Kelly with 7 minutes left in the third period to create a tight finish.
Ray Emery made his third start in the last four games for the Senators and had 26 saves. The loss was the third straight for the Senators, who have yet to win since acquiring Cory Stillman and Mike Commodore in a trade with the Carolina Hurricanes six days ago.
"We didn't get off to a good start at all and to give them a lead makes it tough," Senators captain Daniel Alfredsson said. "We came back hard in the last two periods and we had our chances but three goals behind is tough these days."
The Devils led 1-0 after the opening period on a goal that was originally credited to John Madden. Replays showed Alfredsson directed the puck into his own net as he tried to block a centering pass from Asham.
Asham added his second goal early in the second period when he moved in over the Senators blue-line and wired a slap shot past Emery.
That lead was nearly increased to 3-0 on a Devils' power play, but Parise sent the puck through the crease while facing an open net. Seconds later he had another opportunity at the side of the goal and made no mistake putting the puck up high over Emery.
Late in the period the Senators got on the board thanks to a rare mistake by Brodeur. The normally sure-handed netminder lost the puck behind his net to Alfredsson, who fed Spezza in front of the empty net.
That goal gave the Senators some life, but a solid Brodeur kept the score 3-1 heading into the final period.
"We started to pick it up in the second period and eventually Spezza scored on a play from below the goal line and we fed off of that," Senators coach John Paddock said.
The Senators outshot the Devils 32-20 over the final two periods and 39-29 overall. A bounce here or there could have resulted in a much different outcome.
"I like the way we battled back but we've got to be ready to play games," said Kelly, who now has at least 10 goals in each of the past three seasons.
"We've got to simplify our game and play a solid 60 minutes and until we do that there are going to be long nights for us."
Devils left winger Sergei Brylin has appeared in 305 straight games, giving him the fourth longest such streak in franchise history. Ken Daneyko holds the club record by playing in 388 straight games from Nov. 4, 1989 to March 29, 1994. ... The Senators recorded their 24th consecutive sellout and their 28th in 31 home dates this season.