After the previous week's defeat to St Johnstone in their opening fixture, coach Stevie Campbell had a more experienced side at his disposal.
Included in the side as overage players were Mark Millar and Ryan Dow and both proved highly influential in plotting Killie's downfall.
Only three of side that lost the previous week started and understandably it took United time to settle.
That said, the only threat to the United goal came midway through the first half when a William Gros shot was blocked by the feet of home keeper Joe McGovern.
On 29 minutes, United almost took lead when Ryan Gauld curled the ball just past after great play between Dow and Dale Hilson.
And seven minutes from the break another good move brought United the lead.
Dow played Hilson in on the keeper and though Kyle Letheren blocked it, the ball broke to Jordan Moore who netted.
Just before the hour mark, United increased their lead as Dow's delightfully flighted free-kick was headed home by Ryan Lindie.
However, Killie pulled one back after 68 minutes when Thomson nodded the ball over McGovern.
But it didn't knock United out of their stride and five minutes later John Souttar got on the end of a Hilson cross to stab the ball home.
United's increasing fluency brought them a deserved fourth, Gauld knocking in a Dow cross from the left at the near post.
Dundee United: McGovern, Robertson, Souttar, Barrett, Lundie, Gauld, Millar, Petrie, Dow, Moore, Hilson.
Substitutes: Anderson, Gilmour, Bell, Smith, Fraser, Allan, M Russell
Kilmarnock: Letheren, Barbour, Pursehouse, Slater Hainey 67), Ashcroft, Fisher, Thomson, Davidson, Muirfield (McNeil 67), O'Hara (Hodge 78), Gros.
Substitutes: Mackay.