The Dons were made to pay for some poor finishing with Fraser Fyvie and Lee Miller both guilty of missing excellent chances before Argentinian striker Casalinuovo found the net for the visitors on the half-hour mark.
United midfielder Gomis doubled the lead five minutes later with a smart finish from the edge of the box to condemn Mark McGhee's side to their first home defeat since the opening day of the season.
The Dons asserted themselves more in the second period but never looked like scoring the goal which would have brought them back into the match.
Former Rangers full-back Maurice Ross made his debut for Aberdeen with Jerel Ifil also returning to the heart of the Dons defence.
Danny Cadamarteri, Dundee United's top scorer with four goals, returned for United as did midfielder Prince Buaben following his suspension.
The home side should have taken the lead within 60 seconds of kick-off when Fyvie latched on to Sean Dillon's short headed pass back but the 16-year-old failed to hit the target with only Nicky Weaver to beat.
Cadamarteri, the former Everton striker, turned Ifil with ease at the other end but his smart left-foot strike hit Jamie Langfield's post after nine minutes.
Miller was the next player to spurn a good opportunity when his quick feet earned him a yard of space from his marker Dillon but the Dons striker's composure deserted him at the final moment as he lashed a wild effort over the crossbar.
Cadamarteri continued his lively start with a well-struck drive from distance that brought a fine save out of Langfield.
The visitors did take the lead from the resulting set-piece with Garry Kenneth flicking Mark Fotheringham's cross into the path of Casalinuovo who deflected the ball home.
Craig Levein's men doubled their advantage five minutes later when Gomis pounced on a loose ball on the edge of the box and drilled the ball into the bottom corner with his weaker right foot giving Langfield no chance.
Jennison Myrie-Williams almost gave the visitors a sensational third in the opening minute of the second period when he skipped past two players before unleashing a powerful left-foot strike from 25 yards that went inches past the post.
McGhee made a double change after 54 minutes with Sone Aluko and Chris Maguire replacing Peter Pawlett and Michael Paton who had both failed to impose themselves on the game.
Aberdeen were living dangerously and were fortunate when a corner from Myrie-Williams found Kenneth who headed agonisingly wide after 59 minutes.
A cross-cum-shot from Charlie Mulgrew needed to be pushed over the bar by Weaver for a fruitless corner after 69 minutes as the Dons looked for a way back into the game.
Substitute Aluko could have clawed a goal back for the hosts but his right-foot shot trickled past the post.
Weaver did well to thwart Aberdeen substitute Darren Mackie, who had come on for Richard Foster, in the closing stages.
And there was still time for Miller and Darren Dods to both be shown yellow cards following a heated exchange in the United penalty area before the full-time whistle was met with a chorus of boos from the frustrated home fans.