Brunson spearheaded a sensational second-half rally that saw New York overturn a 14-point third-quarter deficit before surging to a 121-113 win that gives New York a commanding 3-1 lead in the best-of-seven series.
A potentially fatal defeat for Boston was exacerbated by a serious injury to forward Jayson Tatum, who looked distraught as he was carried off the Madison Square Garden hardwood in the fourth quarter.
Tatum, who had been magnificent to that point with a 42-point display, was later seen being ferried to the locker room in a wheelchair.
As the Celtics digested defeat and the brutal Tatum injury blow, the Knicks were left celebrating and eyeing a place in the Eastern Conference finals for the first time since the 1998-1999 season.
"Just found a way to make plays and get us going," Brunson said afterwards of the second-half revival that set up the Knicks' win.
"I was just in a flow and doing whatever. I wasn't really trying to take over. It was just 'whatever we've gotta do'," Brunson told ESPN.
"We didn't quit, kept fighting. And that's what's most important. Whenever you get in a hole, you can't quit."
Boston started the game where they had left off in a convincing game three victory on Saturday, with Tatum and Payton Pritchard swiftly finding their range from outside the arc.
Tatum and Pritchard both scored three-pointers as Boston closed the first quarter on a 12-0 run to surge into a 39-28 lead.
They carried that 11-point advantage into half-time, Tatum finishing with 20 points to help the Celtics to 62-51 at the break.
A Derrick White three-pointer gave Boston their biggest lead of the night early in the fourth quarter, the point guard putting the Celtics 14 points up at 72-58. Then he came back again to drain his sixth three of the night.
But just when it looked as if Boston were threatening to pull away, the Knicks flicked the switch at both ends of the court to kickstart a dramatic rally.
Brunson poured in 18 points as the Knicks roared back to outscore Boston 37-23 in the third quarter and take an 88-85 lead into the final frame.
Brunson kept the points flowing in the fourth quarter, and when OG Anunoby grabbed a steal off Tatum in the incident that left the Celtics star writhing in pain before making a dunk, the Knicks were home and dry at 118-106 with less than two minutes remaining.
Game 5 in the series takes place in Boston on Wednesday, May 14th.