On-loan Wolves striker Leigh Griffiths had given Hibs hope of a first win under new boss Pat Fenlon when he opened the scoring after 24 minutes but United dominated the second half and scored a deserved equaliser through Russell after 59 minutes.
Daly nodded home Paul Dixon's cross with 76 minutes gone before slotting home his second with only two minutes left as United moved into the top six of the Scottish Premier League.
Griffiths returned to the Hibernian starting line-up after missing the 1-0 defeat to Aberdeen after being given a one-match ban for making a gesture to Rangers fans.
Garry O'Connor was a notable absentee for the visitors after picking up a toe injury in the defeat at Pittodrie, while Icelandic midfielder Victor Palsson came in for Danny Galbraith.
New signing Eoin Doyle sat out the match as he is not eligible to make his debut until the January 2 derby clash against Hearts.
Dundee United were unchanged from the side that drew 1-1 with Kilmarnock last weekend with midfielder Scott Allan, who looks set to leave for West Brom in January, handed a place on the bench.
The match started at a lively pace with Johnny Russell firing over from the edge of the box in the opening minute before Ivan Sproule ended a darting run at the other end with a low drive into the side-netting three minutes later.
The hosts were next to carve out an opening after 14 minutes when left-back Paul Dixon floated an inviting ball to the back post but Daly was unable to apply the finishing touch.
Martin Scott showed great agility to take the ball on the chest and fire a volleyed pass across goal into the direction of his strike partner Griffiths, but the former Dundee attacker was inches away from connecting.
However, the duo combined to great effect after 24 minutes when Griffiths raced onto Scott's lofted pass and volleyed the ball calmly past Dusan Pernis to open the scoring.
United almost got back on level terms after 31 minutes when John Rankin and Daly combined to set up Russell who skipped past Paul Hanlon before slotting the ball just past the post.
The visitors almost increased their advantage three minutes before the break but Pernis produced a wonderful save to deny a Griffiths header.
United came out for the second half eager to get back on level terms with Gavin Gunning testing Graham Stack from distance before Scott Robertson was denied by a fine save after 52 minutes.
And the equaliser arrived after 59 minutes when Gary Mackay-Steven slalomed past a couple of Hibernian defenders before finding Stuart Armstrong on the edge of the box. He neatly played the ball into the path of Russell, who rounded Stack before tapping the ball into the unguarded net.
Peter Houston's men continued to dominate, with Dixon finding Russell unmarked 20 yards out but the striker's left-foot volley flew wildly over the top.
And United gained the advantage with under 15 minutes left as Daly rose highest to head home Dixon's enticing delivery.
The visitors came painfully close to getting back on level terms in the closing stages when Hanlon headed just past the post from a Griffiths corner, before Pernis somehow managed to keep out a low drilled effort from substitute Galbraith.
And Daly made sure of all three points when he beat the Hibs offside trap to race onto a Rankin header and slot the ball home with two minutes remaining.