Daly headed home in the 37th minute and Dennis Wyness missed a glaring chance to level just after half-time.
Saints then struggled to break the visitors down but Stephen McGinn hit the bar just before Daly sealed three Scottish Premier League points with a late penalty.
United boss Craig Levein freshened his side up after picking up just one point from games against Kilmarnock and Hamilton, with Danny Swanson, Michael Kovacevic and Garry Kenneth coming in.
Victory for Hearts over Rangers in the early kick-off had left the visitors six points off third spot and United set out in determined fashion.
The St Mirren defence, which had Scott Cuthbert in for the injured Will Haining, was immediately under pressure and goalkeeper Mark Howard came to their rescue in the first minute.
Francisco Sandaza flicked on Morgaro Gomis' cross for Daly, who stretched to volley the ball goalwards, but Howard pushed it away on his line.
Daly headed over from another Gomis cross moments later but St Mirren soon found their feet and Andy Dorman threatened twice.
The midfielder's volley from the edge of the area hit Wyness and looped over Lukasz Zaluska but onto the roof of the net.
Dorman then met Dargo's headed lay-off following a great break from McGinn but his 20-yard volley was too high.
The visitors came back into it but Swanson and Gomis both produced weak efforts when presented with half-chances.
Dorman had St Mirren's best opportunity of the half when he ran on to Wyness' brilliant lofted through ball. The midfielder bore down on goal but Kovacevic came across to make a crucial sliding tackle.
Saints found themselves behind two minutes later when Daly powerfully met Flood's right-wing cross 10 yards out and Howard could only help it into the top corner.
Wyness, who has not scored since notching in Inverness' 4-0 win win over Gretna in October last year, missed his chance six minutes into the second half.
Franco Miranda's pass released Dargo on the left side of the box and he rolled the ball square to the unmarked Wyness, who sliced the ball well wide from 10 yards.
St Mirren were struggling to break United down but Dorman took matters into his own hands by surging 25 yards with the ball at his feet, only for Kenneth to make a brilliant sliding tackle inside the box.
Saints boss Gus MacPherson brought on Steven Robb, Jim Hamilton and Billy Mehmet but hi side still lacked any spark going forward, and United looked increasingly threatening.
Flood's diving header flashed just wide after substitute Craig Conway had beaten Jack Ross and crossed to the near post.
Scott Robertson then beat two men inside the box and dinked the ball over Howard but inches beyond the far post.
Hamilton showed St Mirren's desperation in the 76th minute when he fell over theatrically as he and Zaluska went head to head, with referee Calum Murray booking the striker for his reaction.
Howard pushed wide Daly's powerful first-time strike from 20 yards as United looked comfortable but St Mirren suddenly created some chances.
McGinn volleyed across goal and against the bar from 12 yards after a knockdown from Mehmet, who soon blazed well wide from even closer in after Hamilton's cutback.
St Mirren's comeback hopes ended in the 89th minute when Daly struck a penalty into the bottom corner after Ross had brought down Conway.
Hamilton's win over Kilmarnock made a bad day even worse for Saints as they tumbled to the bottom of the table.