Steven Gerrard's men made it eight consecutive wins in the Scottish Premiership with a 2-1 victory as they were made to work for the three points at Tannadice.
James Tavernier gave the visitors the lead with a world-class free-kick but they were soon pegged back with Liam Smith equalising for the hosts after a deep cross from Jamie Robson.
The league leaders pushed themselves in front for good a minute before half-time as Tavernier turned provider, crossing for Connor Goldson to head home.
Player ratings scale - 10: One of best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: Terrible day at office. 2: Abysmal. 1: One of worst performances you've seen.