The home side came out and took control and took the lead after 50 minutes. A Harris cross bounced off a Dundee defender perfectly for Basham to slide in and direct the ball into the corner of the net, giving Letheren no chance.
Basham then turned provider as United added a third on 65 minutes. A mix up between Letheren and McAlister saw Basham in the clear but he found Baxter who tapped the ball into an empty net.
Sub McNulty handed his debut and the Scottish striker took just two minutes to make an impression. The ball was loose in the box from a Davies corner and McNulty flicked the ball home from a yard, despite a crowded goal-line.
With six minutes left Thomas Konrad pulled one back when he forced the ball home after a corner to make the final score 4-2.
Likely the changes at half-time changed the game Manager Paul Hartley will be happy enough with the first half performance. Next up is Peterhead at Dens Park on Saturday in the League Cup.
Dundee: Letheren, McGinn, Dyer, Benedictus, Konrad, McBride, Thomson, Harkins, Roberts, McGowan, Tankulic. Subs: Adam, Ferry, McAlister, Dodd, Boyle, Kerr, Wighton.
Att: 3,207