With Celtic having wrapped up the league title weeks ago, Dundee had more to play for in this match and guaranteed qualification for next season's Europa League through Scott Robinson.

The 27-year-old headed home Paul Dixon's cross on 21 minutes to claim a priceless victory.

United managed only one shot on goal for the entire game and despite Celtic's continued efforts, they were unable to make a break through.

Elsewhere, Hearts defeated St Johnstone 2-0 in their final home game of the season.

Rudi Skacel converted a cross from Australian Ryan McGowan after 21 minutes to take his season tally to 16 goals before Andy Webster struck from close range to add a second for Hearts just before the hour mark.

Hearts' win moves them two points above St Johnstone into fifth and the visitors must now beat Rangers and hope Celtic beat the capital club to have any chance of finishing fifth.