United made the hosts pay moments later when Flood sent a beautiful cross into the box and Daly rose to head home powerfully.
St Mirren's Denis Wyness spurned a great chance after the break when he blazed over from eight yards.
Scott Robertson lit up an otherwise poor second half when he beat two men inside the box and chipped the ball over Howard but it drifted wide.
The hosts' hopes of rescuing a point were dashed in the final minute when United were awarded a penalty.
Ross was adjudged to have fouled Conway in the box and Daly took the spot-kick to net his and United's second goal of the game.
St Mirren manager Gus MacPherson:
"We're disappointed with aspects of today's performance. There were too many loose balls in the first half and we didn't win enough individual battles.
"I asked for a reaction in the second half and we clearly got that. We created some chances but it's about putting the ball in the net.
"Last season, Andy Dorman would've scored that chance. But it changes so quickly. United win possession in the middle of the park and we soon find ourselves one down.
"That's the fine line in football at this level. When the chances come along, you have to take them."
Dundee Utd manager Craig Levein:
"That was a big game for us. After taking just one point from two matches it was really important we got back on track.
"It's always a tough place to play and get points. I think we maybe just edged it in terms of chances.
"We started the game exceptionally well. As the game wears on you try to protect your lead and we got deeper and deeper.
"St Mirren had a couple of chances, and to be fair, the one that Denis Wyness missed, the ball did bobble.
"It was a really competitive match and I'm happy we got the points."
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