Dundee started well and Lyall Cameron forced a good save from Connor Roberts in the home goal, Paul McGowan forced a even better save soon after as Dundee looked to take the lead.
The New saints had struggled but came into the game and matched Dundee but both teams failed to get the vital first goal. After 34 minutes Paul McMullan went off injured being replaced by Zach Robinson.
Dundee started the second half in good form and took the lead when Roberts failed to clear and Jordan Marshall raced to nutmeg Danial's and his cross was headed home by Cillian Sheridan it took a slight deflection going in but it put Dundee ahead in the cup tie.
The game was well in Dundee's control three minutes later when good quick move and passes from Anderson , Williamson and Sheridan the ball fell to Robinson who fed Kerr to shoot and Lyall Cameron finished the job for a fine goal.
The next 20 minutes were all Dundee , but they failed to add to the scoreline. TNS had a wee spell and Legzdins saved well and they also hit the bar.
Zak Rudden and Luke Strachan came on near the end and it was Luke's debut for the first team.
In injury time Dundee scored their third goal when Robinson broke quickly and set up Max Anderson who finished to score a fine gaol.
Dundee were well in control and the fans who travelled down would go home happy.
Dundee: Legzdins, Kerr, McGhee (c), Ashcroft, Marshall (Sweeney 74), Williamson (Robertson 83), McGowan, Anderson, McMullan (Robinson 34), Cameron (Strachan 83), Sheridan (Rudden 74)
Unused Subs: Lawlor (gk), Sharp (gk), French.
