First half goals by striker Gary Hooper and midfielder Victor Wanyama gave the home side a comfortable interval lead but Tannadice midfielder John Rankin pulled a goal back five minutes after the break.
It was an uneasy second half for Neil Lennon's side but they did enough to leapfrog the champions who had beaten St Johnstone 2-1 at McDiarmid Park earlier in the day.
Source: PA
Source: PA