The Grecians, who climbed up to fifth place in the League Table table in the process, opened the scoring in the 14 minute with their first attack of the game courtesy of a calamitous own goal from Alex Rodman.
The on-loan winger somehow managed to divert the ball past a motionless Michael Ingham in the area with John O'Flynn ready to shoot.
York's response was immediate as they levelled five minutes later through Michael Potts, who was first to react to find an empty net following Artur Krysiak's save from Matty Blair.
Eight minutes after the restart Exeter regained the lead through Jimmy Keohane's strike. Kevin Amankwaah's cross from the right found the winger at the back post and his effort managed to squirm under Ingham's body.
The hosts almost levelled proceedings in the closing stages with Blair chipping wide of the target with Krysiak out of his goal, before substitute Lanre Oyebanjo saw his goalbound effort blocked by defender Craig Woodman.
