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, with Colin Nish serving a suspension, 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.
United had won 3-0 at Tannadice in August in the first competitive Dundee derby for more than seven years and also triumphed by the same scoreline in a sell-out friendly at Dens Park in July.
Both sets of fans in the 11,419 crowd paid tribute to former United captain and chairman Doug Smith, who died on Wednesday, with a minute's applause before kick-off.
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.
Douglas was soon booked for a bad tackle on Riley, but Dundee left-back Matt Lockwood could not take advantage of the free-kick or another soon after.
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.
Watson almost doubled the tally when he let fly with a powerful effort from 30 yards that Rab Douglas only just managed to palm over the crossbar and Johnny Russell soon glanced Douglas's cross just wide.
Milne had a less clear-cut chance after smart play from McAlister and Baird, but hit a weak shot straight at Cierzniak from 22 yards.
Baird then fired over from further out when Dundee had men forward after a United counter-attack broke down.
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.
Milne got on the end of Baird's cross and the ball seemed to come off McLean's raised arm, but Willie Collum played on and Milne could only steer the rebound into Cierzniak's hands.
Russell then cracked a shot off the post from 18 yards after a naive attempted clearance from Declan Gallagher.
Dundee were being restricted to long-range efforts although Lockwood produced a fantastic strike from a 30-yard free-kick, which Cierzniak dived at full stretch to tip over his top corner.
Dundee were running out of ideas and the game went beyond them in the 71st minute when referee Collum pointed to the spot.
Douglas saved from Daly after Armstrong had charged down Kevin McBride's clearance and cut the ball back, but Irvine had gone in late on the United midfielder.
Daly had another chance to beat Douglas and guided the penalty far enough away from the former Scotland goalkeeper's 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.
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- Steven Milne