Crow, thrust into the action from the 15th minute when the Cobblers' top scorer Scott McGleish left the field with a suspected dislocated shoulder, came up trumps with a neat chip over Chris Weale a minute from time.
It was rough on the Yeovil goalkeeper who had pulled off a number of fine saves, but no more than Northampton deserved for their part in an entertaining contest.
Before he left the field, McGleish twice went close, firstly with a fourth minute overhead kick that was tipped over the crossbar and it was those acrobatics which caused his injury. The same player also forced Weale's into another first-rate stop in the 12th minute.
The division's top scorer, Phil Jevons, produced a moment of brilliance in the 21st minute with a cracking 20-yard drive which bounced off the top of the home crossbar.
Ten minutes later, the visitors went ahead when a cross by Lee Johnson was tucked home at the near post by Arron Davies, his second goal in four days.
Yeovil almost made it 2-0 in the 36th minute when Andy Lindegaard's low driven free-kick was met by Rory Fallon but his shot was expertly tipped over the bar by Lee Harper in the Cobblers goal.
But the home side hit back and were close to turning around on level terms only for Tommy Jaszczun to see his left-foot shot rebound back from a post.
Yeovil seemed content to protect their lead in the second half, although it needed another outstanding save by Weale to deny Crow in the 62nd minute as the striker raced clear. Even then, the ball rolled towards an unguarded net only for Terry Skiverton to hack it clear.
But the Glovers' policy of protecting their lead saw them take off both forwards Fallon and Jevons, and they were made to pay when the Cobblers grabbed their late sucker-punch.