Gareth Southgate named a largely second-string outfit at the Estadi Nacional but it had no problem dispatching a side ranked 153 places lower, Ben Chilwell setting the visitors on their way in the 17th minute with his first international goal.
Bukayo Saka added a second before half-time, while Tammy Abraham, James Ward-Prowse and Jack Grealish scored his first international goal to seal the most routine of wins in the second period.
Well… About time 😅 an absolute dream to score my first England goal 🦁 well done boys! Great performance! ❤️ pic.twitter.com/Ea10Hb4P9H— Jack Grealish (@JackGrealish) October 9, 2021
Grealish's goal came in his 16th appearance for his country, and the Manchester City winger acknowledged the drought had been on his mind.
"It has been a long time coming, and it's about time that I scored because everyone has been saying it to me," Grealish said.
"I think that is 16 games now. It was coming, and I'm just delighted that I've got off the mark.
"I want to be starting games, to be starting the biggest of games and keep playing for England. Luckily over the past few months and during the Euros I've had the chance to do that.
"In the back of my mind there has been that feeling that I've just wanted to score, just to get off the mark. Obviously I've done that tonight, I'm delighted, and it's a night I won't forget."
For Abraham, meanwhile, it was his first England goal for almost two years.
The Roma striker became the first England player to score while affiliated to an Italian team since David Platt, then with Sampdoria, netted against Sweden in 1995.
"I need to keep performing for my club and I hope I'll be in more camps going forward leading to the World Cup," Abraham said.
"It is never straightforward against Andorra. It was hard to break them down, but you could see the quality in the team as we had to find ways to score, and we did.
"I knew the opportunity would come. Jadon [Sancho] told me at half-time that sometimes he would cut back on his right and try and find me in the middle of the goal, so I should be ready.
"I was ready that time and got a good toe onto the ball. I was in the right place at the right time and I took my chance."
A sixth win in seven group games means England moves on to 19 points at the top of the group, while Andorra remains in fifth with three points.
Bottom side San Marino was also thumped 5-0 by Poland in Warsaw, and the hosts will look to steal second place in the group from Albania when they meet on Wednesday (AEDT).
England meets fourth-placed Hungary on the same day, looking to cement further its place at the top of the standings.