Caley Thistle jumped above Motherwell into second place in the Clydesdale Bank Premier League after a double from Billy McKay and goals from Owain Tudur Jones and Andrew Shinnie maintained their impressive form.
Inverness have now struck 53 goals in all three competitions, which they retain an interest in, and equalled their 42-goal total from their last SPL campaign at the halfway point of this season. But Butcher often cut a frustrated figure during the game as moves broke down.
However, the Inverness boss was relieved to overcome Dundee, who matched their hosts until Iain Davidson's short backpass three minutes after the interval allowed McKay to beat Rab Douglas at the second attempt and put the Highlanders 3-1 up.
SPL top scorer McKay, who has 18 goals this season, had opened the scoring against the run of play with an 11th-minute penalty after Declan Gallagher had barged Richie Foran but Nicky Riley levelled with a good touch and finish in the 19th minute.
Parity only lasted five minutes until Tudur Jones fired home from 25 yards and Inverness were in control after McKay's second with Shinnie's solo goal the result of a steady stream of chances if not the tide of pressure Butcher wanted.
"Dundee made it very hard for us. I think they are a good side, I can't believe they are at the bottom of the league," he said.
"They caused us a lot of problems, good movement up front, the two wide men did well, backed up by the midfield players.
"I was really worried about today's game because it's one we were probably expected to win, which is very unusual for us.
"We were third and they are bottom but it doesn't matter where we are because we are still playing an SPL team and they have got quality, and they showed that at times...We had to get the goals and the goals came at the right time for us."
- Sports & Recreation
- Owain Tudur Jones
- Clydesdale Bank Premier League
- Andrew Shinnie