Great Britain defeated Portugal 3-0 in their opening Fed Cup Euro/Africa Zone Group I match.
Anna Keothavong beat Maria Joao Koehler 6-3 6-4 before Elena Baltacha saw off Michelle Larcher de Brito 6-2 6-3 to seal the tie, being played in Israel.
Heather Watson and Laura Robson then defeated Koehler and Larcher de Brito 7-5 6-0 in their doubles match.
"Today was fantastic," said Judy Murray after her first match as captain. "We did not drop a set."
Great Britain take on the Dutch in their second group match on Thursday.
And Murray added: "We've got a tough one against the Netherlands but we've prepared well and we'll be ready."
Baltacha was pleased by the form shown both by herself and Keothavong.
She said: "We knew it wasn't going to be easy because the Portuguese girls have done well in the past.
"I think sometimes with girls at that level you're never too sure which one of them is going to turn up, as in you don't really know what kind of game they're going to bring. But Anne and I knew that we'd have to stick to our guns and get the job done which was the most important thing."
GB hope to qualify from the week-long Euro/Africa Group I competition in Israel.
The format sees 15 nations form four round-robin pools, played from Wednesday to Friday. The nations that finish top in each pool will go through to the promotion play-offs, which take place on Saturday.
The two winning teams will go through to the World Group II play-offs, while the bottom nations contest the relegation play-offs to decide which two teams are relegated to Euro/Africa Group II.