Held 3-3 at halftime, Wales blitzed the visitors with 24 points in the opening 17 points of the second half as Scotland were punished for having centre Nick de Luca and fullback Rory Lamont sent to the sin-bin.
Alex Cuthbert went over for Wales' first try in the 42nd minute before Halfpenny crossed twice in a seven-minute span to maintain his team's perfect record, after last weekend's 23-21 win in Ireland.
"We came in at halftime a bit frustrated but we knew if we kept the ball we could put them under pressure and the points and tries would come," said Halfpenny, who also kicked two penalties and three conversions.
Greig Laidlaw scored all of Scotland's points through a try, a conversion and two penalties.
But while Wales can look forward to a match with fierce rivals England - the only other team with two wins from two so far - at Twickenham in a fortnight's time, Scotland are again facing the prospect of a battle with Italy to avoid the wooden spoon.
Andy Robinson's team squandered a raft of chances when losing 13-6 to England at home last weekend but it was their indiscipline that cost them dear at the Millennium Stadium.
"Yellow cards are always crucial, you've got to be squeaky clean in this day and age and everybody's got to work on their discipline," said Wales flanker Dan Lydiate.
Cuthbert had just gone over for a converted try down the right wing when De Luca was yellow-carded for tackling rival centre Jonathan Davies off the ball.
Scotland conceded 10 points while De Luca was in the sin-bin, Halfpenny booting a penalty and then running on to a pass by Cuthbert for his first try, to fall 20-6 behind by the 51st.
Lamont was also given a yellow card for not releasing No 8 Toby Faletau after the tackle but De Luca was back on the pitch by the time Halfpenny looped round the back of scrumhalf Mike Phillips to go over in the corner.
"Scotland came back into it and it was touch and go, at the end we were under the cosh," Lydiate said. "But we're delighted with the win and we've got to be confident going into that game against England."
Laidlaw touched down for the Scots' first try in five matches in the 64th but they couldn't make any further inroads.
"After halftime, we missed the restart and Wales took their opportunities," Robinson said. "Credit to Wales - they had chances and took them and we had chances and we didn't.
"We played very well and we're hurting and disappointed."