First-half goals from strike partners Dele Adebola and Kevin Kyle ensured Dowie's tenure as Sky Blues boss got off to a winning start.
Dowie's first decision was to install the injury-free Elliott Ward as captain instead of Robert Page who was missing with a knee problem.
The new manager had a perfect start when Coventry went in front in the fifth minute.
Andy Marshall's goal kick was expertly headed on by Kyle to Adebola and the striker lashed a powerful strike into the corner of the net from 15 yards.
The fourth-placed Saints put their hosts under pressure when Kenwyne Jones challenged Marshall in the air and when the ball dropped near the line, Colin Hawkins cleared the danger.
David McNamee was harshly shown a yellow card for fouling Jones 30 yards from goal and Gareth Bale stepped up to take the free-kick but the 17-year-old's strike took a deflection off the wall.
Southampton equalised from the resulting corner in the 13th minute. Bale swung the ball over from the right and Jones' header was headed off the line by Kyle. The ball came back into the box, and when Marshall fumbled the clearance, Marek Saganowski prodded in a close-range shot for his first goal for the club.
Coventry continued to attack and played with more energy and vision than in their recent poor spell which has seen the club win just one of their last 13 games.
And they were rewarded by re-taking the lead in the 29th minute. Michael Doyle's fantastic cross from the left fell perfectly to Kyle to arch a superb header over keeper Kelvin Davis.
Doyle started another fine move for the home team by teeing up Andy Whing and his right-wing centre was hit into the side-netting by Kyle.
The visitors responded when Bale released Jones and he went on a mazy run before unleashing a firm shot which was deflected wide.
George Burley made two substitutions at the start of the second half when he replaced Rudi Skacel and Pele with Djamel Belmadi and Alexander Ostlund.
Dowie was forced into a change eight minutes later when Isaac Osbourne came on for the injured McNamee.
Coventry were awarded a free-kick just outside the area and Stephen Hughes curled a low shot beyond the wall and the far post.
Southampton put the Sky Blues under increasing pressure with Bale proving a major threat. He first of all sent over a far post cross which Jones knocked just wide and the teenager then dispossessed Osbourne to unleash a shot which Marshall blocked.
The injured Jay Tabb was replaced by Leon McKenzie and the mis-firing Jones was substituted for leading scorer Grzegorz Rasiak with 12 minutes remaining but Southampton team were unable to prevent Dowie from experiencing that winning feeling just 36 hours after taking over at the Ricoh Arena.