Both sides scored within the opening six minutes at Tottenham Hotspur Stadium, where Isak won it with a 38th-minute goal.
The Swede pounced on Radu Dragusin's mistake to put Newcastle in front as Eddie Howe's side completed the turnaround after Solanke's opener.
Spurs' defensive issues came back to bite when Gordon restored parity just 140 seconds later and Isak then scored for a seventh league game running.
Spurs hit the post through Brennan Johnson after the break, before James Maddison's curling attempt flashed wide and Solanke sent a looping header onto the roof of the net late on.
Newcastle held firm and after a lengthy period of second-half stoppage-time, got over the line to consolidate its place in fifth, while Spurs remain in the bottom half.
Ange Postecoglou's side, which has now gone six league games without a home win for the first time since October 2008, also finished the game without a recognised centre-back after Radu Dragusin was removed at half-time with an injury.
"On the balance of play, any balance you want with all things being equal, we would have won," the Australian coach said.
"Outstanding. I couldn't be prouder of the players. I couldn't ask any more. It's a game we would have won if all things were equal.
"If all things were equal and balanced, we would have won. Things weren't equal and balanced."
When asked if it was Newcastle's first goal that was not equal, he added: "You can talk about whatever you want. You want my opinion – if all things were equal and balanced, we would have won.
"We had plenty of chances. Our football was outstanding considering everything we're going through.
Conversely morale is high at Newcastle and coach Howe is sure his side can continue building on its positive momentum.
"Confidence has definitely shifted, it naturally does when you win games," Howe said. "It was something we were building to.