After falling behind to an early strike from Archie Collins, the Robins put in a valiant display to find the net through Alfie May, Liam Sercombe, Andrew Williams and Will Boyle.
The Grecians took the lead after four minutes when 21-year-old Collins snatched the ball in the middle of the field and drove towards goal. Having beaten several defenders, Collins fired a shot from the edge of the penalty area and saw his effort take a wicked deflection to trickle past Town ‘keeper Joshua Griffiths.
Jonathan Maxted kept Exeter’s advantage intact with a fantastic stop from a close-range header. His work was not done, however, and the 28-year-old had to react quickly to palm the ball off the line and away from danger.
It was a lead that was to only last three minutes, as the Robins drew level through Sercombe, who put the ball high into the top corner after being first to a teasing ball from Finn Azaz.
Cheltenham completed the turnaround just under 10 minutes from when they went behind. May smashed home a rebound on the second time of asking after some slack defending had allowed a long ball into the box.
Unsettled by the comeback, Exeter dropped in intensity and began to rush their build-up with reckless long balls forward, much to the delight of the boisterous Town supporters. Confident pressing kept City penned back in their own half, resorting to desperately-smashed clearances in order to keep the deficit at one.
The Robins came very close to doubling their advantage on the brink of halftime when goalscorer May beat the onrushing Maxted to a loose ball and guided it around the goalkeeper, but the awkward angle he found himself at did not afford an opportunity to shoot.
Cheltenham forward George Lloyd was cynically brought down in the final action of the first half. Referee Bobby Madley pointed to the spot with no hesitation. Sercombe stepped up to take the penalty and made no mistake, smashing it straight down the middle for his second goal of the afternoon.
Exeter began the second half a much brighter outfit than the one that had trudged to the changing rooms 15 minutes earlier. Randell Williams linked up well with target striker Ryan Bowman, but they were kept at bay by savvy goalkeeping from Griffiths.
City then finally got the goal they had been threatening 10 minutes after the restart through Jay. The in-form 24-year-old tucked the finish neatly across the goalkeeper from 10 yards out after receiving a perfectly-weighted delivery from substitute Nicky Law.
Cheltenham never faltered, though, and the Robins ploughed on, dominating the game as time wore on. Their lead was restored through substitute Williams. The ball was not cleared following a corner, and the 34-year-old reacted first to find the net in front of the home terrace.
Law threw his side a lifeline with two minutes left to play when he drove excellently on a counterattack and slotted beautifully into the bottom-left corner. It was not one that lasted long as Scottish defender Boyle put Cheltenham back in control.
The result keeps Cheltenham in good stead in second in the League Two standings, one point behind Newport County at the top. Exeter, meanwhile, fall to fifth place.
Home advantage is back
Fans returned to the Jonny-Rocks Stadium for the first time in 274 days, and the difference the atmosphere made was clear to see.
Not once did Cheltenham look off-the-pace, nor did they ever slow down their incisive approach play.
League Two has seen some adverse scorelines in recent weeks, but they can be expected to cease with the return of home support.
Exeter too reliant on attack
Matt Taylor appears to have City playing an ‘if you score three, we will score four’ philosophy, which has suited them well until now.
Cheltenham, who are enjoying their best-ever start to a season, exposed the blemishes in Exeter’s defence and severely punished them for it.
Often a lapse in awareness allowed the hosts in behind, and, in some areas, the Grecians were fortunate to keep the ball away from their goal.
Man of the Match
Alfie May - Cheltenham Town
Robins forward Alfie May takes the man of the match award for an inspired attacking performance.
Operating largely on the right flank, the 27-year-old posed a threat to Exeter each time he got hold of the ball, and, of course, bagged Cheltenham’s opening goal.