Saints were well worth their victory, but had fallen behind against the run of play to Darren Mackie's 17th minute strike.
Kenny Deuchar capitalised on a Jamie Langfield error to head his side level, before on-loan Celtic striker Sheridan netted a low strike five minutes later.
Another mistake from Langfield allowed Sheridan to bag the third with 25 minutes to go.
Aberdeen lined up for their final game before the SPL split, making just one change from the side that had been beaten by Rangers at Ibrox in midweek.
Former Manchester City man Paul Marshall came in for his first start since February, replacing Sone Aluko, who dropped out completely. Davide Grassi started despite a facial injury picked up in midweek.
Full-back Danny Grainger started a ban for the Saints, while fellow defender Dave MacKay missed out through injury.
Former Celtic man Gary Irvine came into the defence, while midfielder Murray Davidson's return from suspension saw Liam Craig fill in for Grainger at left-back.
Both sides will end the season in the bottom six, but St Johnstone have earned praise for the form that has seen them rise to seventh place, four points ahead of today's hosts.
Pittodrie basked in sunshine as the teams lined up for a minutes' applause in honour of Dons legend Zoltan Varga, who died aged 65 in his native Hungary this week.
Saints settled into the game quickly, and they had the first real chance after 12 minutes when Chris Millar's cross from the right found Deuchar in space, but he headed wide.
The Aberdeen fans claimed a penalty when Mackie tumbled under pressure from Michael Duberry, but there was nothing in the challenge.
It was Mackie who stroked his side in front after 17 minutes. Duberry failed to clear, and Marshall slid in Mackie who sidefooted home with ease.
However, St Johnstone were level within four minutes. Langfield failed to claim Craig's free-kick, and Deuchar looped a header into the net from 15 yards.
The game was turned on its head as St Johnstone went in front five minutes later.
Zander Diamond missed his header, allowing Jody Morris to slip a neat pass through to Sheridan and he turned the ball home from eight yards, beating Langfield at his near post.
Davide Grassi picked up the first booking of the match 10 minutes from the break, as he flew into a challenge on Irvine that did not need to be made.
The Dons came close to levelling three minutes before the interval, Steven MacLean forcing Graeme Smith into a diving save at his near post after Jerel Ifil's cross.
The game remained open after the interval, but both sides were again finding clear-cut chances hard to come by.
Aberdeen were gifted an opportunity when referee Calum Murray penalised Steven Anderson for handball inches outside the area, substitute Derek Young curling the free-kick narrowly over the bar.
However, St Johnstone extended their lead after 65 minutes.
Langfield failed to deal with Deuchar's flick from another Craig free-kick, and the ball fell kindly for Sheridan to fire into the top corner from six yards.
Saints keeper Smith did well to block from substitute Fraser Fyvie after Mackie's pass.
That sparked a late flurry as the Dons looked for a way back, but they could not find a way past a staunch St Johnstone rearguard, although Richard Foster sent an effort wide from 20 yards.
Teenager Jack Grimmer had a late effort for the hosts, but saw the ball spin away of the legs of a defender for a corner.