Galbraith, who had never scored a league goal before, had only been on the field for eight minutes when he collected a loose ball 30 yards out when David Rowson's corner was cleared, and the young defender advanced before cracking home a terrific left-foot drive.
It meant that these sides repeated the scoreline they managed earlier in the season and Cobblers' boss Colin Calderwood at least had some measure of celebration for his 40th birthday next week.
Darlington, now unbeaten in their last four games, had gone ahead in the seventh minute with American midfielder Adolfo Gregorio on target for the second Saturday running - his first goals for the North East club.
But the opener was a disaster for home defender Tommy Jaszczun who was robbed by Clyde Wijnhard and the former Leeds man pulled the ball back to Gregorio who came steaming in to score with a low drive.
Northampton showed no signs of missing the creative influence of Martin Smith and Josh Low who have been a feature of their recent form which has brought just one league defeat in 10 starts.
Sam Russell was in excellent form in the visitor's goal and he made a brilliant 23rd minute save when Charlie Hearn's corner was met by the head of Eric Sabin only for the goalkeeper to push away the powerful effort.
Northampton doubled their efforts after the restart when top-scorer Scott McGleish volleyed over the crossbar and Trevor Benjamin saw a venomous free-kick deflected over the bar.
But when Benjamin was thwarted on the near post by Russell in the 73rd minute it looked as though Darlington would escape with the spoils.
That was the signal for Galbraith to cap a heated finale which also saw visitor's boss David Hodgson sent from the dug out.
Darlington's only other significant chance saw Wijnhard go clear six minutes before the break but he chipped a shot wide of the target.