It was a timely display by the 21-year-old, coming one day after coach Fernando Santos said he still had many doubts over the starting line-up for their opening World Cup match against Spain on June 15.
The European champions also face Iran and Morocco in their first-round group while Algeria, who reached the round of 16 in 2014, failed to qualify for Russia.
Portugal made a lively start and Cristiano Ronaldo, playing in his first match since the Champions League final on May 26, had a goal disallowed after he was caught fractionally offside.
Guedes, with nine appearances and one goal before Thursday, fired Portugal in the front in the 17th minute after William Carvalho hit a long ball over the Algeria defence and the lively Bernando Silva cushioned a header invitingly into his path.
Ronaldo set up the second in the 37th minute when he sped down the left and provided a pinpoint cross which Bruno Fernandes met with a powerful downward header for his first international goal.
A similar move led to the third goal as Raphael Guerreiro burst down the left and Guedes met his cross with a bullet header into the roof of the net in the 55th minute.
Portugal's defence, which has looked ponderous in recent matches, coped well with Algeria's attacking threat and Rui Patricio had to make only one save, from substitute Baghdad Bounedjah.
"There were some good things and a lot to improve, but the first 20 minutes were very good," said coach Santos, who refused to give anything away about his starting line-up.
"The 23 are all ready to play, that is the most important thing."
(Writing by Brian Homewood, editing by Ed Osmond)
