After a dour first half in which the NFC East rivals were only able to trade field goals, the New York Giants finally broke the game open halfway through the third quarter in New Jersey on a 36-yard touchdown run from running back Saquon Barkley.
The Cowboys immediately hit back through a one-yard touchdown rush from back Ezekiel Elliott, before Lamb's spectacular reception in the end zone put Dallas in front with 8:34 left on the clock.
A quick exchange of field goals kept things close, but a late interception from Giants quarterback Daniel Jones ultimately sealed New York's first loss of the season.
Dallas quarterback Cooper Rush posted 215 yards through the air and a touchdown, while Jones finished with 196 passing yards to go along with 79 yards on the ground.
Speaking after the game, Lamb told NFL.com: "I was willing to do anything to make up for a touchdown potentially that I left in the first quarter.
"It was tough. It was a tough one. But I'm happy we came out victorious."
Looking back at the fourth down which led to his touchdown, Lamb added: "Without it, I don't get no touchdown. Conversions, we preach toughness and willingness, and I was willing to put my body out on the line.
"But all the other ten guys and the guys that are one the sideline, they're believing in me. They trust my talent and so do I. Them guys have my back the whole game."