The Tannadice striker popped up to head home his 11th goal of the season and leave Saints to think of what might have been after Liam Craig missed a 70th-minute penalty.
The hosts had held the slight edge in a competitive Tayside derby when Craig saw his kick saved by Dusan Pernis.
Daly made Craig pay for his failure as Peter Houston’s men extended their unbeaten run to eight games and opened up a commanding eight-point lead over Hibernian in the pursuit of the Europa League.
But Derek McInnes’ side now face a massive fight to reach the top half, trailing Hearts by three points ahead of the last round of pre-split fixtures this weekend.
Houston made one change from the team that won 4-2 at Hibs, with Paul Dixon restored after suspension for Prince Buaben. Fit-again Danny Cadamarteri was also among the substitutes.
St Johnstone were unchanged from the team that stunned leaders Rangers 4-1 and created early pressure, forcing five corners in the opening 10 minutes as they adapted best to the blustery conditions.
They came closest when top scorer Craig tried his luck from distance and Pernis took no chances to push over.
United threatened after 15 minutes when Craig Conway’s free-kick from the left saw the ball break to captain Andy Webster, who brought out a smart save from Graeme Smith from 10 yards.
At the other end, a glorious opening fell to Jody Morris. Filipe Morais’ free-kick was nodded into the Londoner’s path by Michael Duberry but Morris fired wide from just inside the penalty area.
Saints came yet closer when Danny Grainger’s cross drifted across goal and Pernis had to look lively to smother Sheridan’s effort at his far post.
Ex-United defender Grainger was lucky not to join Michael Duberry in referee Steve Conroy’s book after a rash challenge on Danny Swanson.
United almost made a stunning start to the second half as Dixon’s cross from the left was flicked on by David Goodwillie and Daly stretched to knock over Smith’s bar.
The visitors had resumed in far more positive fashion as a strong away support voiced their approval.
On 52 minutes, Webster looked certain to score but was flagged offside before Smith impressively turned over his drive anyhow.
Neat footwork from Chris Millar saw Saints respond but Pernis was behind his curling strike.
Houston was forced into a change on 56 minutes as ex-Saint Darren Dods replaced the injured Webster.
The hosts immediately passed up their best chance yet as Morais’ left-wing cross fell at the feet of Duberry but the former Chelsea defender lashed wide from the penalty spot.
Craig then saw a lofted half-volley drift over Pernis’ bar as they began to exert more pressure.
Buaben made his entrance on 67 minutes for Goodwillie, while ex-United forward Collin Samuel replaced Sheridan.
Just two minutes later McInnes’ side were handed the perfect chance to break the deadlock.
Dixon tripped Dave Mackay in the area and Conroy had no option but to point to the spot.
However, Craig picked the wrong time to miss his first penalty of the season as Pernis dived to his left to push away.
United’s players rushed to congratulate their Slovak goalkeeper, but home heads did not go down.
Mackay soon went close when his acrobatic half-volley almost drifted into the far corner of the net, but the visitors withstood the pressure to claim the decisive goal against the run of play seven minutes from time.
Morgaro Gomis did brilliantly on the right to dig out a cross and Daly was on hand to bullet a header past Smith. Saints pushed for the leveller but Houston’s outfit held on for a precious victory.