United were on the front-foot early on, with openings falling to both Brian Cash and Sean Kelly, but Brendan Clarke dealt comfortably with both efforts.
Rovers had a fifth-minute penalty appeal waved away by referee Damien Hancock, despite Shaun Kelly appearing to have tripped Iarflaith Davoren in the box, but most of the early action was at the other end, with Alan Murphy trying his luck from distance, but his sliced effort was well wide.
It took the visitors a while to settle, but once they got their passing game going, they began to dominate. John Russell was pulling the strings against his home-town club, and it was he who set up the opener.
Jason McGuinness launched a long ball forward, and Russell outpaced the United defence to pick out Dillon in the box.
He took a touch, turned inside past Stephen Walsh and fired home from 10 yards for his third league goal in two games.
Russell went close to extending the Rovers lead on the hour after being put through by Matthew Blinkhorn, but Greg Fleming got a strong hand to his well-hit shot, while Dillon then hit the woodwork with a blistering drive.
It was not all one-way traffic as United forced a succession of corners, but the Sligo defence eventually managed to scramble the ball clear, but it was the visitors who were the more threatening, and Russell popped up in the United box again but his shot was cleared off the line by Shaun Maher.
United battled hard but lacked any cutting edge up front, and it was the visitors who looked most likely to score, but they couldn’t add the second goal their display deserved.
Aaron Green had two glorious chances late on, but he was denied by a cracking last-ditch tackle by Shaun Kelly in the 82nd minute, and then fired wide with only Fleming to beat after skating through a hesitant United defence in the final minute.
GALWAY UNITED: Fleming; Shaun Kelly, Maher, Sinnott, Walsh; Cash, Sean Kelly, Murphy (inj, Feeney 83), Moore; Ryan; Yoffe (Curran 76).
SLIGO ROVERS: Clarke; Keane, Peers, McGuinness, Davoren; Dillon (Ndo 83), Ryan, Russell, Greene; Kirby (Ventre 65); Blinkhorn (Doyle 76).
Referee: Damien Hancock (Dublin).