Henderson scored his first two goals in three minutes around the half-hour. but held back the full drama until the sixth minute of added-on time.
Bristol City thought they had salvaged a draw seconds before when Costa Rican Alvaro Saborio scored after coming on as a late sub.
United threw everything into a quick break from the restart and from the left of goal Henderson placed his shot accurately into the far bottom corner.
For his first two strikes - he now has ten this season - he needed a little outside help as City slipped to their first home League defeat for almost a year.
Referee Andy Hall overruled a linesman flagging for offside after the first goal. His second was set up by Bristol centre-back Jamie McCombe with a timid mis-kick which would have looked bad in a pub Sunday League.
The offside claim came after Dean Gerken in punching a ball away stumbled past United's Lee Williamson, before being beaten by Henderson's return with Williamson in an offside position.
Energetic in their approach work, City were fading badly in the final quarter and United came under the biggest threat in the first half from two free-kicks given away by Andy Davies. But then when the lively Danny Haynes got past him, Davies tackled back strongly to snuff out the threat.
City got into the game early in the second half when striker Nicky Maynard was fouled 45 yards out on the left. Paul Hartley swung the kick towards the far post and his captain Louis Carey raced through from the back line to head past Carl Ikeme.
The Sheffield keeper went on to make significant saves from Maynard and Haynes, but had little chance with the late equaliser as Saborio got on the end of one of many high balls pumped into his area.