Two of Watson's four previous goals came in the Europa League and another in a victory over Rangers and the right-back settled United down after a difficult start when he headed the opening goal in the 17th minute.
Dundee lacked bite up front but Steven Milne squandered an excellent first-half chance and they had a strong penalty claim denied when Brian McLean appeared to handle. But they looked devoid of ideas before United put the game beyond them in the final 20 minutes through Jon Daly's penalty and a soft late goal from Willo Flood.
The home side made the far brighter start. Wide players Nicky Riley and Jim McAlister made enterprising runs into box and striker John Baird looked lively in the opening stages. The pressure only produced one effort on goal when Riley headed just over from 20 yards after Radoslaw Cierzniak punched away a corner.
United took quarter of an hour to make an attack of note and they scored from their second corner moments later. Barry Douglas swung the ball out towards the near post and Watson peeled off his man to stoop and head home via a deflection.
The hosts created a great chance around the half-hour mark when McAlister headed Gary Irvine's cross into the path of the unmarked Milne but the forward volleyed over from 10 yards.
Rob Douglas got down well to save from Stuart Armstrong seconds after the restart but United then had an escape when McLean appeared to handle inside the box.
Russell then cracked a shot off the post from 18 yards after a naive attempted clearance from Declan Gallagher.
Dundee were running out of ideas and the game went beyond them in the 71st minute when Willie Collum pointed to the spot after Irvine brought down Stuart Armstrong. Daly guided the penalty far enough away from Douglas' dive.
United matched their previous scoreline in the 88th minute when Flood took the ball from Armstrong 18 yards out and hit a weak effort that bobbled over the outstretched arm of Douglas and trundled home.
Source: PA
Source: PA