Team Europe moved 8-6 ahead in the race to 11 as they edge towards a third straight Mosconi Cup triumph.
Shaw picked up the last point of the day after putting on a classy display against USA's Dominguez.
The Scotsman, who has a propensity to play his best pool at this event, lit up Las Vegas by taking the opening two racks.
Dominguez didn't appear rattled by the start as he slowly but surely worked his way back into the contest.
The 37-year-old was able to claim back-to-back racks and levelled the match to the delight of the home crowd.
However, Shaw saved his best pool till last as he picked up the next three points to seal a potentially crucial victory for the European team.
Before dispatching the final nineball, Shaw sparked wild celebrations from the visiting fans.
After potting, the celebrations continued as Europe took a two-point lead in the race for the Mosconi Cup.
Speaking to Sky Sports, Shaw said: "It was a big point. I played well. Did what I had to do. We've got the lead. Go away, refocus and get the team right for tomorrow.
"Obviously the pressure was on. I always deliver when the pressure is on. That's what I do, that's what I live for, these big moments."
With the loud European contingent behind him, Shaw added: "It's all about these guys. We need you tomorrow. Come on!
"Obviously they're loud [USA fans] so when we get one on the board we've got to be just as loud as them."
Photo Credit: Matchroom Pool