On the stroke of hal- time, Forest Green Rovers keeper Steve Williams and defender Alex Lawless got their wires crossed and Stansfield nipped in to slot home from close range.
It was the one bright spot of a poor first half during which neither side managed to create anything note-worthy in front of goal.
Exeter City were dealt a blow after it emerged that last season's leading goal scorer Lee Phillips had failed to fully recover from an ankle injury and would have to be content with a place on the bench.
City boss Paul Tisdale had thrown down the gauntlet to his side to turn St James Park into a fortress this season in a bid to boost their promotion hopes.
Inside the first minute, Stansfield almost converted Billy Jones' deep cross as the Grecians sought an early advantage. Rovers defender Lawless then produced a magnificent block to deny Jon Challinor and Rob Edwards sent a header across the face of the Rovers box.
The home side suffered a scare when keeper Martin Rice failed to collect Simon Clist's corner and Mark Preece sent a looping header over the bar. Alex Meechan then watched his fierce shot breeze past the post as the visitors looked to hit on the counter-attack.
Tempers spilled over when Michael Brough scythed down Chris Todd and Challinor got into trouble for a late tackle on Meechan.
With half-time looming City were gifted the lead thanks to a defensive mix-up in the Rovers rearguard after Williams and Lawless failed to clear, Stansfield raced clear to steer into an empty net.
The visitors came close to scoring an equaliser shortly after the interval when Allan Russell's header was hooked off the line by City defender Danny Woodards.
Then Jamie Pitman forced Rice into a smart stop following a long-range effort.
Challinor found his way into the referee's notebook after being cautioned for timewasting. St James Park erupted when Phillips bounced back from an ankle injury to play his first game in three weeks by coming off the bench.
The striker almost made an immediate impact when he produced a pinpoint cross into the feet of Challinor, but the midfielder wasted the chance with a poor first touch.
The Grecians started to take a stranglehold on the match and Andy Taylor was denied when his fearsome shot rattled the crossbar.
Stansfield squandered a chance to settle the outcome - and claim his second goal of the game when he nicked the ball off Tony Butler on the edge of the penalty area and bore down on goal.
The lively frontman attempted to slot the ball between the keepers' legs and it deflected into the path of Phillips whose subsequent shot was turned around the post. City continued to crank up the pressure and pepper the Rovers goal with Phillips again denied following a magnificent goal-line clearance from Lawless.
Despite a late Rovers rally the City defence held firm and celebrated their first three points of the season after an opening day draw at York City.
The Grecians have yet to concede a goal after collecting four points from their opening two games and they have a golden opportunity to continue that momentum when Altrincham are the visitors to St James Park on Saturday.