The midfielder, making his second league start of the campaign, fired an unstoppable shot past Eldin Jakupovic to seal victory for City in the second half at the Etihad.
They had earlier taken the lead through Ahmed Elmohamady’s own goal, the Hull defender turning into his own net after 31 minutes.
Sergio Aguero doubled their advantage shortly after half-time and Delph blasted home their third on 64 minutes before a mistake by Claudio Bravo allowed Andrea Ranocchia to score a late consolation.
The result keeps Man City in fourth and extends their lead over Arsenal and Manchester United to seven points, although both clubs hold two games in hand on Pep Guardiola’s side.
United travel to Sunderland on Super Sunday, while Arsenal visit Crystal Palace on Monday Night Football.
As for Hull, they remain two points above the relegation zone after 18th-place Swansea lost 1-0 at West Ham on Saturday.
Guardiola made four changes from the 2-1 defeat at Chelsea but retained Delph after praising his performance at Stamford Bridge.
His opposite number Marco Silva handed Michael Dawson his first league start since February in place of the injured Harry Maguire, while Evandro came in for Abel Hernandez.
His Tigers were on the back foot almost immediately and had Jakupovic to thank for a fine double save after just four minutes.
The Hull stopper initially denied David Silva on his 300th Man City appearance before reacting quickly to keep out Leroy Sane’s follow-up effort.
Aguero went close from distance as did Yaya Toure with a curling free-kick before Man City made their possession count.
Jesus Navas’ fine attacking display was rewarded when the Spaniard’s cross was turned into his own goal by the hapless Elmohamady.
It was Hull’s fifth own goal of the season but the visitors responded well and had the chance to reply immediately through Oumar Niasse.
The striker found himself unmarked in front of goal but miscued wide following good work by the lively Kamil Grosicki.
That missed opportunity proved costly as City swiftly extended their lead after the break.
Sterling, who was excellent throughout, teed up Aguero and the Argentine made no mistake, netting his 10th goal in his last 10 appearances.
Man City’s third also came courtesy of a Sterling assist but owed more to the quality of Delph’s strike. The midfielder received a pass 25 yards from goal and unleashed a fierce drive into the far corner.
Hull pulled one back through Ranocchia with five minutes to play as the Italian’s first-time finish squirmed past Bravo.
Having had little to do for much of the match it was an inauspicious finish to the game for the Chilean, who was preferred to Willy Caballero.
In the end it mattered little to the result, which puts the onus back on Arsenal and Man Utd in the race for Champions League qualification.
Man City travel to Southampton next Saturday while Hull visit Stoke.
