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 City in the table, with the Robins seeing a run of three straight wins abruptly ended at the KC Stadium.
Source: PA
Source: PA