A wonderful volley from Saints midfielder Andy Dorman after 28 minutes had given the home side a deserved lead and they looked odds-on to move six points clear of bottom side Falkirk.
However, a minute into added time in the first half the Scotland international levelled when he drove past Buddies keeper Mark Howard.
A entertaining second half saw Hibs stopper Gregorz Szamotulski dive smartly to his left to stop midfielder Denes Rosa scoring an own goal, before Howard produced a brilliant reflex save from defender Sol Bamba.
While the Paisley side should have no relegation problems on this display, the Easter Road side are now one point ahead of Motherwell in sixth place with one game remaining before the SPL splits in two, although title-chasing Rangers travel to Edinburgh next week.
Around 1,000 local children had been allowed into the ground free of charge in an attempt to bolster the atmosphere and it was certainly lively enough in the early stages as both sides went flat out for the opener.
Slowly the tide turned in favour of Saints who probed down the right-hand side with a measure of success without managing to get through to test Szamotulski.
Despite the lack of real goalmouth action, there was plenty to keep the crowd entertained and as the first half unfolded Hibs began to emerge as a threat.
Bamba, booked earlier for a foul on Stephen McGinn, headed a Derek Riordan corner high over the bar when he might have been expected to hit the target.
However, in the 28th minute the Paisley side opened the scoring with a wonderful strike from Dorman.
After another spell of St Mirren pressure, the ball was fed out to the edge of the box by McGinn to the Saints midfielder who volleyed past the helpless Szamotulski for his 10th goal of the season.
With three minutes remaining Riordan got the break of the ball at the edge of the box but never looked in control as he volleyed wide.
It appeared the Buddies would go into the break with a well-deserved lead but in the first minute of added time, they let slip their concentration and found themselves level.
Fletcher raced on to a Riordan pass and with no little confidence the Scotland striker drove past Howard for the equaliser.
The home side must have sat stunned in the dressing room but they looked to have shrugged off that disappointment when the second half began.
Once again St Mirren looked sharper and more determined and it was Dorman, surprisingly, who missed a decent chance four minutes after the restart when he sliced wide from close range after Szamotulski had spilled the ball at his feet.
Two minutes later, after some erratic passing from both sides, Fletcher picked up an Alan O'Brien pass 30 yards from goal, turned and drove just over the bar.
Veteran Paisley striker Jim Hamilton replaced Billy Mehmet in the 56th minute before Hibs substitute Jonathan Johansson came on for O'Brien, but still the game remained finely balanced.
As play swept from end to end, Hugh Murray had the ball in the Hibs net soon after the hour mark with a sweet volley from Hamilton's lofted cross but was ruled offside.
In the 66th minute Szamotulski had to move quickly to his left to stop Rosa putting Dorman's cross into his own net from six yards out.
The Hibs goal was temporarily under siege as Saints went up another gear in search of the winner but in the 77th minute Howard pulled off a fantastic reflex save from Bamba who had latched on to an in-swinging free-kick to glance in a close-range header.
From Riordan's subsequent corner, Bamba headed off the bar with the ball falling into the hands of the Saints keeper.
St Mirren came back again and with four minutes remaining striker Craig Dargo should have met Ross's perfect cross from the right with more conviction.
However, the former Inverness player mistimed his effort and the ball flew wide, and with that went the last real chance of the game.