With rookie tight end Jeremy Shockey sidelined in the first half with turf toe, Collins hit veteran Dan Campbell with a 20-yard pass on third and three to advance to the Dallas 18. Two plays later, Rivers recorded his vital first catch of the season
"It was just a basic post route," Rivers said. "I was able to get a step on the defensive back and Kerry made a great pass. It feels good to contribute in any way I can."
The Giants offense had produced just three touchdowns this season entering Sunday and was held to fewer than 10 points in back-to-back games against Seattle and Arizona.
"I've been reminded all week about my touchdown-to-interception ratio (1-to-6), so it was nice," Collins said. "We stepped up and made plays the way we needed to. To be able to come through in the fourth quarter like that for a score, it says a lot."
Toomer finished as the Giants' leading receiver with five catches for 98 yards.
Collins completed 18 of 27 passes for 228 yards with an interception. The veteran signal caller has posted a 64.0 completion percentage this season after recording a 54.6 mark in his previous seven NFL campaigns.
"I thought he made excellent choices today," Giants coach Jim Fassel said. "We really balanced our offense today. I didn't want to rely on the big plays, like the long pass or the red-zone offense. We did well today and I am pleased."
Dallas defensive tackle Michael Myers swiped at Collins in the backfield and caused a fumbled exchange with running back Ron Dayne, which was recovered by defensive end Ebenezer Ekuban.
On the ensuing drive, Cowboys quarterback Quincy Carter found rookie Antonio Bryant in the back of the end zone from five yards out, putting them in front, 17-14 with less than 11 minutes to play.
Dallas (2-3) lost for the fourth time in its last five meetings with its NFC East rival.
"This is a game of big plays," Cowboys Coach Dave Campo said. "They made theirs and we didn't. We did a poor job of stopping them inside the 20 yard line."
Following last week's 21-7 loss at Arizona, Fassel instructed offensive coordinator Sean Payton to simplify the game plan, slashing the number of plays.
"I don't think it was a matter of having more plays or fewer plays," Collins said. "I thought we all were just disappointed with last week. So we just worked harder, stuck with it and played four quarters."
The revised strategy helped New York establish its running game. Averaging 82.2 yards on the ground and a league-low 2.9 per carry in their first four games, the Giants gained 104 yards Sunday.
Tiki Barber picked up 94 yards on 17 carries, including a 23-yard burst on the eventual game-winning drive.
Meanwhile, Collins completed passes to seven different players.
"When you don't score on offense, that puts a lot of pressure on your defense," said Giants defensive end Michael Strahan , who recorded four tackles while frequently attracting double coverage. "It's encouraging because those guys had a lot of pressure on them going into the game."
While Rivers stepped up in Shockey's absence, Giants backup cornerback Ralph Brown was victimized by the Cowboys, who should have regained the lead with less than three minutes left.
William Peterson, who made interceptions late against St. Louis and Seattle to clinch the Giants' previous two victories this season, left the game with an injury. In his place, Brown was flagged for pass interference, giving the Cowboys a first down near midfield down the stretch.
On the next play, Bryant put a move on Brown and blew by him down the left sideline, but Carter overthrew him on what appeared to be a certain touchdown pass.
"Players make plays when they have to. I didn't make one when I needed to," Carter said. "We had opportunities to win that game and we didn't get it done. When you lose, it is hard to take anything away from it."
Emmitt Smith , the Cowboys' star running back who averaged 59 yards in his first four games, ran for 70 yards on 13 carries. His performance was highlighted by a 30-yard TD run, his first of the year, which knotted the contest at 7-7 with 5:40 to go in the first.
Smith needs 234 yards to surpass Walter Payton (16,726) as the NFL's all-time leading rusher.
Celebrity Couples of 2014 [PHOTOS]