Billy McKay scored for a seventh consecutive match as he claimed a double to send Caley Thistle back into second in the SPL.
Inverness have now scored 42 SPL goals, equalling last season's final total exactly at the halfway point of the campaign.
Butcher said: "I'm just delighted it's another win and we have scored a good number of goals again. We could have had more, (Dundee goalkeeper) Rab Douglas has had a great game.
"If you had said at the start of the season, by Christmas we would be second in the league, I would have said you have had a few glasses. But we are where we are and we will certainly enjoy Christmas."
McKay took his tally for the season to 18 with a penalty opener and the crucial third goal, which finished off the previously spirited resistance of Dundee three minutes after the break, when he scored from the ground after failing to take the ball past Douglas.
A long-range strike from Owain Tudur Jones, which put the hosts 2-1 ahead in the 24th minute, and a solo effort from Andrew Shinnie took Caley Thistle past the half-century mark to 53 goals in all competitions.
Dundee gave as good as they got in the first half but conceded from Tudur Jones' effort five minutes after Nicky Riley had levelled with an impressive finish. And they shot themselves in the foot three minutes after the interval when Iain Davidson's back pass set up McKay.
Manager Barry Smith said: "We thought we had created enough chances in the first half to possibly go in level. Obviously the third goal makes it a lot more difficult and they go from strength to strength."
Smith had few complaints about the penalty, given for Declan Gallagher's barge on Richie Foran, and he said: "I have not seen it again but I think, when I do, it probably is one."
- Sports & Recreation
- Caley Thistle