Charlton's on loan keeper Scott Carson, aided by a string of astonishing misses, had kept United at bay for almost the entire game until the winger slammed in a stunning 25-yard volley to seal a vital win for the Sheffield side and leave Charlton still propping up the Premiership.
United, fresh from their win at relegation rivals Watford in midweek, almost snatched the lead in the second minute.
Rob Hulse picked out Stephen Quinn but the youngster lashed a fierce left-foot strike straight at Carson.
Christian Nade had a shot blocked after neat work by Gillespie before the Blades squandered a chance after winning a throw in deep in the Charlton half.
Leigh Bromby's long throw was met by centre-back Chris Morgan who flicked the ball into the goalmouth. Hulse reacted instantly but pulled his header wide of the target from six yards.
Charlton made United pay in the 17th minute as ex-Spurs midfielder Andy Reid surged towards the United are before passing inside to Darren Ambrose. Republic of Ireland goalkeeper Paddy Kenny pulled off a one-handed save to push away his close-range strike, but the ball fell to Reid who swept it past the stranded keeper.
Morgan almost levelled matters minutes later as he jumped to meet a Gillespie corner but Carson, who was unsighted, dived at the last moment to palm the ball around the woodwork.
United pressed for the equaliser and Derek Geary's low cross was headed on by Hulse but the ball flashed past the post with Nade slow to react. Phil Jaglielka then ballooned a shot into the stand after the Charlton keeper had punched clear.
Charlton clung on as United turned the screw and Hulse was again denied by Carson who pulled off another eye-catching stop to turn his shot on the run around the post.
But Carson was finally beaten in the 64th minute as Morgan stretched to meet a Gillespie corner to finish with a powerful header from six yards.
And Gillespie then slammed in the winner on 88 minutes as he steamed on to Djimi Traore's clearance to volley past the helpless Carson.