Barry Smith was delighted to see his Dundee side progress in the William Hill Scottish Cup courtesy of two goals early in the first half.
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The Clydesdale Bank Premier League side won 2-0 at Livingston, with their goals from Steven Milne and a Ryan Conroy penalty coming inside the first 17 minutes.
Smith said: "It was a good professional performance by us. Stevie Milne was very sharp and John Baird came in for his first start for a long time.
"It was great for him to put in a performance like that because he's waited for his time, and he did well and got the penalty.
"Although Livingston had a lot of possession, they didn't create too many chances; but credit's due to them for the way they kept the ball, as they kept it very well for spells in the game.
"It was good to get the victory; performances in the league have been decent so hopefully that's the start of another wee run."
Livingston head coach Gareth Evans says his team should have been awarded a "stonewall" penalty at a crucial stage shortly after Dundee's spot-kick, after Liam Fox's shot was handled.
Evans said: "His shot was saved on the line with a hand; at 2-0 the third goal is going to be crucial and it should have gone to us.
"It could have changed the game as we were in the ascendancy for 75 minutes and were the team that passed the ball and had it down palying football, so if we'd got the penalty, who knows what would have happened?
"It's disappointing - the first 15 minutes cost us as we lost a sloppy penalty and another sloppy goal, but after that we looked like the SPL team, passing the football.
"Dundee got the victory and it was obviously a tough game for them coming here, shown by the amount of possession we had - but we need to start turning that into goals."