The hosts were three-up by half-time at Tannadice, Keith Watson putting them in front just four minutes in, before David Goodwillie (25) and Gary Mackay-Steven (40) extended the lead.
Stuart Armstrong (53) added the gloss after the break as they brought Saints back down to earth after their promising start to the season which saw them start the day in second place in the table.
It was a miserable afternoon for former United keeper Steve Banks, who left for St Johnstone in the summer.
He was picking the ball out of the back of the net four minutes in as United got the perfect start against their Tayside rivals.
Ryan Dow's pass found Watson and the full-back advanced on goal and let fly from 22 yards with his left foot and with the help of a slight deflection off Patrick Cregg the ball flew into the far corner.
After 25 minutes, Goodwillie made it 2-0 for the hosts. Dow's free-kick deep into the box found Watson, who nodded on towards Goodwillie and the on-loan Blackburn striker rose majestically to power his header past Banks.
Banks pulled off a brilliant save from Goodwillie's deflected shot three minutes later but on 40, the third did arrive.
Calum Butcher released full-back Andrew Robertson, who raced down the left before slipping in Mackay-Steven, and the winger rolled the ball calmly under the advancing Banks.
Nigel Hasselbaink almost pulled one back after the break but his shot from 10 yards was too close to home keeper Radoslaw Cierzniak.
But after 52 minutes, United sealed the points. Dow slid the ball wide to the all-action Mackay-Steven, who in turn crossed for Armstrong.
Armstrong timed his run to perfection from midfield and although his shot hit the ground, it bounced up and over the stranded Banks.
The hosts saw the game out with ease from there to secure a first win of the season for boss Jackie McNamara.