Hull skipper Hobbs, last on target while on loan at Leicester in January 2009, headed his side into a 13th-minute lead, Slovenia international Robert Koren added a second two minutes later and Matty Fryatt made sure of the points with his first goal in over two months on the hour mark.
Nick Barmby’s side dropped out of the play-off places after their scheduled game at Portsmouth last week was postponed, but a third win in their last four league matches keeps them in the chasing pack.
Bristol City are currently in freefall, their steady climb following the arrival of Derek McInnes in October apparently in reverse after four defeats in their last five.
Barmby made just one change, recalling Robbie Brady up front alongside Fryatt, while defender Lewin Nyatanga, winger Jamal Campbell-Ryce and midfielder Marvin Elliott returned for Bristol City.
Fryatt pulled a 25-yard shot off target in the 11th minute, but Hull took the lead in their next attack.
Koren crossed from the right and central defender Hobbs, who staggered in the penalty area at the moment of contact, managed to direct the ball goalwards with his head and it bobbled over visiting goalkeeper David James and the goalline.
The Tigers doubled their lead in more impressive fashion two minutes later.
Brady this time supplied a telling cross from the right and Koren was first to react, steering his header beyond James into the bottom corner from 12 yards.
Bristol City, who ended last week with nine men in the home defeat to Leeds, were dealt another blow in the 22nd minute when midfielder Kalifa Cisse was forced off through injury and replaced by Ryan McGivern.
But the visitors responded in style and almost pulled a goal back when Albert Adomah’s angled drive hit the crossbar in the 26th minute.
Hull immediately stormed down the other end and Koren forced a fine save from James with a snapshot from inside the area as the game burst into life.
Koren forced James into another superb save after cutting in from the right and unleashing a shot from 25 yards, but there were no more goals before the break.
Eight-goal Fryatt, who has gone over two months without scoring, was denied by James at full stretch and the visitors’ goalkeeper held Cameron Stewart’s volley as Hull continued to dominate.
Hull were rewarded for incessant pressure with a third goal on the hour mark.
Koren again did all the damage down the right and his ball into the area was swept home by Fryatt, right-footed, into the bottom corner.
Bristol City striker Stephen Pearson forced Hull goalkeeper Vito Mannone into a sprawling save with a 25-yard shot in the 75th minute, but James kept out Hull again seven minutes later when substitute Josh King fired in a low shot.