The win maintained their perfect record after five games.
Fernandes' low strike two minutes from half-time beat Martin Dubravka inside his far post as the midfielder marked his 29th birthday with his third goal in the Euro 2024 qualifiers.
Portugal had made a faltering start against Slovakia, who had two good chances inside the opening 15 minutes through forward Robert Polievka and winger Lukas Haraslin.
Haraslin was once more inches away from opening the scoring as the game neared the end of the first half when his curled shot from the edge of the box narrowly missed the right post.
But after Fernandes gave Portugal the lead coach Roberto Martinez's side looked more like their usual selves in the second half, dominating possession and looking to extend their lead while Slovakia did well to keep the deficit to one goal.
Portugal, who host Luxembourg on Monday, have 15 points followed by Slovakia, who have 10 along with third-placed Luxembourg after they beat Iceland 3-1.
Slovakia are bidding to qualify for their third consecutive European finals.
The two teams meet again on October 13 in Porto.
At age 16 years and 57 days, Yamal struck in the 74th minute to round off the rout and bettered Gavi's mark as Spain's previous youngest-ever scorer at 17 years and 10 months.
Yamal had come on as a first-half substitute to become the youngest player to appear for Spain, a record also previously held by Gavi in 2021 when he was 17 years and 62 days.
Spain took a 4-0 lead inside 40 minutes at Boris Paichadze Stadium to move up to second in Group A on six points after three games.
Scotland, who beat Cyprus 3-0, lead the group on 15 points after winning all five of their matches so far.
Morata opened the scoring for Spain in the 22nd and got his second in the 40th. He completed his hat trick in the 65th.
Solomon Kvirkvelia scored an own-goal in the 27th to double Spain's lead and Dani Olmo added another in the 38th.
Giorgi Chakvetadze pulled one back for Georgia four minutes after the break.
After Morata's third made it 5-1, Nico Williams scored a sixth for the visitors in the 68th before Yamal capped a historic evening when the forward converted Williams' cross with a fine left-footed finish.
In other matches, Croatia whipped Latvia 5-0, Turkey drew 1-1 with Armenia while Bosnia and Herzegovina beat Liechtenstein 2-1.