Scott Robertson scored after 32 minutes and John Rankin in second half stoppage time as United leapfrogged their hosts to move within three points of third-placed Motherwell, who meet Celtic on Sunday, meaning Champions League football is a realistic prospect at Tannadice next term.
Saints hit the post in the second minute through Cillian Sheridan, but their cause was hampered after 57 minutes when Francisco Sandaza was sent off after kicking out at Sean Dillon and the top scorer can expect a minimum two-match ban which will hinder the Perth side's quest for European qualification.
Third place should secure a place in the Champions League qualifying stages next term - given Rangers are excluded as a result of their administration - and United are in contention after victory in the first post-split fixture, but there are bound to be twists before their trip to Motherwell on the final day of the season.
Saints can have few complaints and were second best before Sandaza was shown a straight red card by referee Euan Norris, the subject of Celtic boss Neil Lennon's fury at Hampden last week.
Steve Lomas' men may yet be left to rue their performances in Perth this term after a ninth home loss, the most outside of the SPL's bottom two.
Injury and suspension forced Saints into a reshuffle, with Derek Riordan making his debut among five changes, while United were unchanged despite seeing a six-match winning run ended by Aberdeen last time out.
Riordan, the third highest scorer in SPL history, featured on the left wing after signing a short-term deal last month and almost had an immediate impact.
His free-kick from the edge of the area forced Dusan Pernis to save and Sheridan hit the follow-up against the post from a narrow angle.
After Pernis saved from Murray Davidson, the visitors should have gone ahead.
A Gary Mackay-Steven cross was fumbled by Saints goalkeeper Alan Mannus, with Gavin Gunning in close attendance.
The ball broke for Willo Flood, who blasted over from three yards out with Mannus prone on the floor.
United appeared most likely to take the lead after nullifying the threat of Riordan, whose frustration was evident when he complained repeatedly to Norris for a foul.
Flood looked to make amends for his miss and a fine cross from the right found Daly, who uncharacteristically was unable to find the target with a header at the back post.
Moments later, however, United were in front after Saints failed to clear.
Rankin played the ball to Scott Robertson, who found the bottom corner from inside the right edge of the area.
Mannus was unconvincing throughout the first half, not helped by the wet weather and a slippery ball, and almost presented Daly with another United goal when he sliced clear, but the United skipper could not find an opening.
Gunning departed early in the second half after falling heavily on his shoulder before Sandaza followed.
The striker was first booked for dissent and then saw red - there was no second yellow - for lashing out at Dillon, who had fallen to the floor after an aerial challenge.
The Spaniard had to be persuaded from the field by players from both sides.
Marcus Haber, who had appeared set to replace Sandaza, came on for Riordan as Saints opted for fresh legs up front, but it was United who continued to attack.
Daly went close three times before Rankin sealed victory in the third minute of stoppage time after being allowed to make space to shoot left-footed into the bottom corner.