However, the Turk made amends for his miss by latching onto a Hanlon error to open the scoring.
Jordon Forster levelled just before the break, but it proved a temporary reprieve for a Hibs side that collapsed after the break.
Gavin Gunning restored the visitors' lead with a towering header and Tom Taiwo saw red for a second yellow card in the space of 15 minutes.
Farid El Alagui then added some deserved gloss to the score, converting Andrew Robertson's low cross.
The hosts left the field to a chorus of jeers, while Dundee United moved to within seven points of second-placed Aberdeen.
It was United's gifted Turk Ciftci who was first to threaten after 15 minutes, the play-maker's free-kick from distance deflecting against Forster and creeping wide.
Within five minutes the visitors were presented with a golden opportunity to open the scoring as Euan Norris awarded a contentious penalty.
Hanlon was certainly guilty of a clumsy foul on Ryan Dow, but television pictures showed the offence took place outside the area.
Nevertheless, on the advice of his assistant Stuart Macauley, Norris pointed to the spot. But justice was done as Ciftci produced a woeful penalty, with a straight run-up to a side-footed effort which Ben Williams, who stopped six out of the nine spot-kicks he faced last season, easily saved.
Williams was on hand to stop a Ciftci header minutes later, but, with the interval on the horizon, the former Portsmouth youngster finally found his range.
The 22-year-old out-muscled Hanlon inside the area before cutting inside Nelson and calmly slotting past Williams from 10 yards.
There was still time for Hibs to draw level as United keeper Cierzniak flapped at an Alex Harris corner, with his poor clearance rebounding against Forster and looping into the net.
United were immediately on the front foot after the break, with Mackay-Steven scuffing an early opportunity over the bar as he latched on to a Stuart Armstrong delivery.
Ciftci then curled a teasing effort just past the post as the visitors turned the screw.
And United got the goal their pressure deserved on 55 minutes thanks to Gunning. The Irish defender leapt highest to nod home a Mackay-Steven corner for his third goal in two games.
Gunning, who has become a real attacking force for the Tannadice men in recent weeks, then won their second penalty of the night as he was tripped by Nelson.
Mackay-Steven was given the responsibility this time, but he fared no better than Ciftci, blasting his kick wildly into the South Stand.
The miss should have given the home side heart, but their chances of rescuing a point were undermined as Taiwo was given his marching orders for a second booking after scything down Paul Paton.
Their numerical advantage told as the men from Tayside made it three.
Robertson surged down the left to provide a pin-point cross for substitute El Alagui to fire past Williams from close range with his first touch.
There was still time for Stanton to strike a post, but it would have been scant consolation on a miserable night for the hosts.
- Sports & Recreation
- Paul Hanlon
- Nadir Ciftci
- Michael Nelson
- Ben Williams
- Farid El Alagui
- Dundee United