Simpson, who had been enduring a drought in front of goal following his summer move from Arsenal, grabbed his first goal in a Hull shirt in the first half when he finished off some sterling work from Cameron Stewart.
And he doubled his tally midway through the second half when firing home from 15 yards to ensure that Nigel Pearson’s men have now gone six league games without defeat.
Nobody have conceded less goals at home than the Tigers and Bristol City rarely looked like breaching that stingy defence, with Danny Rose’s effort from long distance the nearest they came to registering.
The win sees Hull move above Bristol City in the table, with the Robins seeing a run of three straight wins abruptly ended at the KC Stadium.
The Humberside region has avoided the snow which has decimated the Football League programme this weekend and there were no fears that the game would fall victim to the weather.
The temperatures may have been freezing but Hull began in a hot streak of form and Kamil Zayatte tested David James from a 20-yard free-kick, but the former England goalkeeper was equal to it and turned the ball over.
But it was the visitors that should have led when unmarked Steven Caulker blazed over at the far post from a Craig McAllister corner.
Hull made the most of their reprieve and took the lead in the 13th minute and the goal was made by Stewart.
The on-loan Manchester United youngster went on a driving run down the left side and picked out an inch-perfect cross for Simpson to turn the ball home at the far post.
Stewart was central to everything Hull were doing and he should have doubled their lead in the 26th minute when he was clean through on goal, but he lifted the ball over James and wide of the post.
The lack of quality in the final third from the visitors was telling and Vito Mannone was an untroubled spectator in the Hull goal for the first half.
The on-loan Arsenal stopper was finally called into action after the break as he scrambled to keep out a fizzing 25-yard shot from Rose. The ball went through Mannone’s hands but fortuitously dropped just wide for a corner.
The Robins continued to press for a leveller and David Clarkson had a gilt-edged chance when he failed to get his free header on target, instead glancing over the bar.
However, it was Hull that strengthened their position with Simpson’s second of the game just after the hour.
City defender McAllister tried to clear a through-ball but he only succeeded in setting up Simpson, who had no trouble firing home from 15 yards.
The Robins tried in vain to get back into the game and could have set up a nervy finish but Brett Pitman could not connect properly with Rose’s cross and the danger was averted.