The Paisley side looked set for a deserved triumph at McDiarmid Park before late injury-time drama.
Stephen O'Donnell handled on the line and, after referee Charlie Richmond took minutes to allow the kick to be taken as he sought the St Mirren offender, Sheerin netted.
Graham Carey netted a first-half opener before Andy Dorman added the second five minutes after the interval as Gus MacPherson's side looked poised for a first away victory in six months.
But Michael Duberry pulled one back 11 minutes from time before Derek McInnes' team claimed the dramatic point.
St Mirren were left enraged at Richmond, who had earlier not awarded a penalty for a perceived foul on Billy Mehmet.
MacPherson rang three changes after the 2-1 defeat at Falkirk. Michael Higdon, Garry Brady and Chris Innes all dropped to the bench as Dorman, O'Donnell and Steven Robb came in.
Dave Mackay again missed out for the Perth men due to a calf knock, but Danny Grainger was back from suspension to replace Murray Davidson.
St Johnstone began the brighter with Grainger and Filipe Morais both firing long-range efforts over, the former coming closest from a free-kick.
But St Mirren, whose cause was far greater, quickly responded when O'Donnell neatly turned Grainger in the penalty area before skewing wide.
Midfielder Dorman was playing more advanced just off Mehmet in attack as MacPherson sparked new life into his side.
A scrappy, tense affair soon developed, before Saints passed up a glorious opening on 22 minutes.
Kenny Deuchar won a header at the edge of the area and Duberry cushioned the ball into on-loan Celtic forward Cillian Sheridan's path, who could only shoot over from 12 yards.
St Mirren hit back with their best chance of the half four minutes later. David Barron fed O'Donnell from the right, whose hooked ball saw Dorman strike first time from the penalty spot. His effort looked net-bound but clipped the top of Graeme Smith's bar.
The Paisley side were to have better luck on 33 minutes when they broke the deadlock.
O'Donnell did well to dig out a cross from the right by-line and his centre across goal saw Carey beat Duberry to force home from close range.
McInnes was forced into a first change on 36 minutes as Liam Craig trooped off to be replaced by Davidson.
Four minutes from the interval only the heroics of Smith denied the visitors a second.
Robb's cross from the left was perfect for Dorman whose close-range downward header was stopped by the legs of Smith.
With their tails up, St Mirren claimed a delightful second goal only five minutes after the break.
The impressive Mehmet controlled a long ball upfield, turning brilliantly to play a sweeping ball into the path of the onrushing Dorman.
Smith raced from his goal to narrow the angle, but the Welshman calmly lifted the ball over him and into the empty net from 25 yards.
The hosts were struggling to get any foothold in the game as St Mirren - who soon saw Mehmet's penalty claim turned down by Richmond for a perceived foul by Smith - held the ascendancy.
McInnes made his second substitution on the hour mark as Collin Samuel came on for Sheridan, but they continued to struggle to carve out openings even if Chris Millar saw a deflected shot squirm wide.
St Mirren goalkeeper Paul Gallacher was finally brought into action on 75 minutes as he held Morais' angled drive at his near post.
But, out of the blue, a grandstand finish was set up when Duberry scrambled home his first goal for McInnes' men.
In a penalty box melee, Samuel nodded against the post before Davidson hooked back across goal for Duberry to rise highest to nod in.
O'Donnell headed a yard over at the other end before Samuel pulled just wide as an otherwise tame contest sprang to life.
The visitors looked set to hold on, but an incredible finish saw St Johnstone claim a point.
After a Morais free-kick was not cleared, Davidson's shot was blocked on the line by O'Donnell's arm.
Richmond awarded a penalty but appeared unsure who was the offender and spent fully three minutes discussing with assistant James Bee who was set to be handed a red card.
But, bizarrely, amid furious protests from the visitors, Richmond only booked O'Donnell.
Fully four minutes into stoppage time, substitute Sheerin stepped up to net the spot-kick.
St Mirren protests continued after the final whistle as they vented their fury at Richmond.