Inverness manager Terry Butcher insists was far less comfortable than the scoreline suggests.
But Butcher was delighted with a third straight win and praised his side's recent scoring form.
"It's only comfortable when we get the fourth goal at the end," said Butcher.
"We always score. It's a lovely feeling that we always score. That's 11 goals in the last three games, which is quite some doing."
Early goals by Billy McKay and Gary Warren put the Highlanders in control at Dens Park before Colin Nish pulled one back for the hosts.
Andrew Shinnie netted from the spot after Shane Sutherland had been fouled in the box and McKay added a late fourth.
And Butcher was pleased with how his team responded to the absence of injured captain Richie Foran.
"People that have come into the team have come in and done a great job," added Butcher.
"Everybody's got a great attitude but everybody plays with a smile on their face. They really enjoy the training, they enjoy the games. They know their jobs very well.
"Four-one looks a comfortable win, it certainly wasn't comfortable. Dundee are spirited. At 2-0, we were wondering, 'what's going to happen next?' And then Dundee scored.
"Up until that point, the crowd were against them and things weren't going right for them but right for us. They scored to get back in the game. They pushed us and pushed us and pushed us and we had to defend desperately.
"[Goalkeeper] Tony Reguero had to make some really important saves. I didn't think Dundee were ever out of it at all.
"We kept going in the second half and Andrew Shinnie was on fire and Billy McKay as well."