The centre-back, who formerly played for United, opened the scoring for Hull but his second-half own goal capped a remarkable turnaround from the visitors.
Hull made a dream start with two goals inside the opening 15 minutes. First Chester volleyed home Alex Bruce's knock-back and then David Meyler's shot found its way home via a deflection off Jonny Evans.
But Chris Smalling's header reduced the arrears and a stunning Wayne Rooney volley levelled proceedings with 26 minutes gone.
The goal was Rooney's 150th Premier League strike for United, making him only the second player after Thierry Henry to reach the landmark with one club.
Hull created the better of the second-half openings, with Bruce hitting the crossbar, but United, who finished with 10 men, made it 17 wins from their last 18 Boxing Day fixtures when Chester headed Ashley Young's cross past his own goalkeeper.
Remarkably, Chester nearly earned a point in injury time after Antonio Valencia had been sent off for United, but took a heavy touch in the penalty area, allowing David de Gea to make the save.
United's comeback wrapped up their fifth consecutive win in all competitions, while Hull have gone five games without victory in the top flight.
Hull named the same side for the fourth straight match, while United included Darren Fletcher in their starting XI for the first time since December 1, 2012.
The hosts stormed into the lead as early as the fourth minute. Tom Huddlestone's corner was headed across goal by Bruce and Chester volleyed home from close range.
Replays suggested a corner should not have been awarded as Ahmed Elmohamady had kicked the ball straight out of play.
Hull doubled their advantage nine minutes later to leave the home supporters in dreamland. A bout of pinball in the United box resulted in Meyler's goalbound effort deflecting off Evans and deceiving goalkeeper De Gea.
United needed a swift response and duly delivered after 19 minutes when Rooney's teasing free-kick was headed home by Smalling to halve the deficit.
The visitors twice came close to levelling with a Danny Welbeck header and Tom Cleverley's long-range strike.
And the pressure was rewarded when Rooney played a one-two with Welbeck before teeing himself up for a volley that he rifled into the top corner from 25 yards.
Hull were forced into a change at half-time with goalkeeper Allan McGregor - who was involved in a first-half collision with Welbeck - being replaced by Steve Harper.
The hosts twice forced good opportunities in the early stages of the second half. First Yannick Sagbo had an effort beaten away be De Gea before Curtis Davies glanced Huddlestone's corner wide.
Bruce came even closer just after the hour mark when his header rebounded off the crossbar.
The visitors punished Hull for their profligacy in the 66th minute as Young got past Maynor Figueroa and Chester headed past substitute goalkeeper Harper when under pressure.
Hull pushed for a leveller in the closing stages and Danny Graham should have done better with a tame back-post header.
Valencia added to the tension in injury time when his petulance in kicking the ball away earned him a second yellow card, and Chester almost redeemed himself but saw his late toe-poked effort smuggled to safety.
