United came into the game on the back of 24 consecutive losses against Celtic in all competitions, but the Tangerines never lacked confidence throughout the game and always looked dangerous even when they fell two goals behind midway through the second half.
Former Celtic striker David Fernandez had the first real chance of the match after only four minutes. Barry Robson's chipped ball to the back post was headed back across goal by Grant Brebner and Fernandez was presented with an excellent chance from eight yards, but the Spaniard's shot was well blocked by Adam Virgo.
Despite United's confident start to the match it was John Hartson who fired Celtic in front with his 16th goal of the season.
Former Dundee United player Mark Wilson, making his Celtic debut against his old team-mates following his recent move from Tannadice was fouled by Robson in the lead up to the Celtic goal. Japanese playmaker Shunsuke Nakamura swung over one of his trademark free kicks to the back post where the unmarked Hartson had the easy task of heading home from six yards.
Nakamura's dead ball delivery was troubling the visitors' defence and minutes later, he swung in a dangerous corner that was headed just wide by Stanislav Varga.
But Celtic didn't have it all their own way and they had to rely on a fantastic finger tip save from Artur Boruc after 15 minutes to maintain their advantage. Virgo failed to cut out Robson's cross and Jim McIntyre's header was well touched behind by the keeper low to his right.
Then seconds later, McIntrye laid the ball off to Derek McInnes with a fine cushioned header but the Tangerines skipper sent his shot wide.
Boruc was called upon to make another fine save on the half-hour mark - this time from one of his own players.
Fernandez made a fine turn 25 yards from goal as he shimmied away from Stilian Petrov and Neil Lennon before sliding the ball through to McIntyre. But the pass was cut out by Varga and Boruc had to be alert to stop the big defender knocking the ball into the back of his own net.
United's superiority paid off as Fernandez levelled just before the interval. The Celtic defence was all over the place as they failed to deal with a Robson corner and Fernandez fired home from six yards.
Celtic almost hit back on the stroke of half time as Hartson was denied by a fine save from Derek Stillie.
Celtic re-took the lead at the start of the second half in a similar fashion to the way they opened the scoring early on. Shaun Maloney swung in a free kick from the left flank and the United defence was caught flat-footed as Maciej Zurawski rose unmarked in the area to head past Stillie.
After 55 minutes, Celtic were denied a stonewall penalty as Maloney tumbled inside the box following a crude shoulder charge from Stuart Duff. But referee Mike Ritchie waved away the claims.
United still looked dangerous coming forward and Boruc once again had to be alert to save from Fernandez.
But the league leaders built up a two-goal cushion midway through the second stanza as Petrov netted Celtic's third goal. The Bulgarian's 25-yard effort took a wicked deflection off the outstretched leg of McInnes, wrong footing Stillie and flying into the back of the net.
United introduced Lee Miller for the final 10 minutes as they tried to get back into the match and this instantly paid dividends as he netted within a minute of coming on when he latched onto McIntyre's header before firing home from close range.
Then, with four minutes of the match remaining, the visitors sensationally levelled as Fernandez netted his second goal of the afternoon. Following a neat move, Miller played the ball through to Fernandez, who took the ball round the keeper, before firing into the empty net.