But Federer made a nonsense of such predictions with a vintage display, largely outplaying the Mallorcan in a 7-6 (3) 1-6 6-3 6-4 victory on a spellbound Centre Court.
Williams will face 27-year-old Simona Halep of Romania in Saturday's women's final.
Federer turns 38 next month, while Rafael Nadal is also nearing the end of his glittering career.
Here are some of the reactions.
Bautista Agut was playing his first grand slam semi-final at the age of 31 in a week when he was meant to be on his own stag party in Ibiza.
Federer won his first Wimbledon duel against Djokovic in the 2012 semi-finals but the Serb triumphed in the 2014 and 2015 championship matches.
Federer will be hoping for his ninth Wimbledon title, while Djokovic will be aiming for his fifth.
A 48th career meeting will represent the 16th grand-slam clash between the modern-day greats, with this the fifth to decide a major title.
"Then the climax at the end with the insane last game, some tough rallies there - it had everything at the end, which was great, I guess". It's great to be part of this rivalry among three players.
Federer's eight Wimbledon titles are more than any other man in history and if he beats Djokovic he will match Martina Navratilova's success in women's singles.
"I think at the end of the match I started to play much better, no?"
There are no secrets between Roger Federer and Novak Djokovic, nothing new to learn after 47 matches staring at each other across the net, 15 of them in slam events, nothing to fear except the fear of embarrassment.
'Maleficent' ignites war, finds familiar allies in new trailer
But her terrifying mother figure Maleficent ( Angelina Jolie and her amazingly enhanced cheekbones) isn't so sure about this. Of course, she forbids Aurora to marry, telling her that "love doesn't always end well".
"But at the same time I created another opportunity to be in another final of a Grand Slam".
However, he will have his work cut out on Sunday if he is to secure a 21st major title as he trails 15-time Slam victor Djokovic 25-22 in career meetings.
The first-set battle seemed to have taken the wind out of Federer, who seemed to unravel in a series of errors.
Roger Federer booked his place in Sunday's Wimbledon final with a huge win over Rafael Nadal. "The longer I play the smoother it goes".
"But the nice thing about Roger, I guess, was the first time that we sort of really knew each other was when I presented him with the Australian (Open) trophy when he had won it (in 2006)".
"You go through these kind of emotional moments, especially in big matches like this, all the time", Djokovic said.
"He played a bit better than me, I had a few small chances but didn't convert them."
Federer is the third oldest to play in a Grand Slam final after 39-year-old Ken Rosewall featured in the 1974 Wimbledon and US Open finals.
Soon enough, the defending champion was bellowing and shaking his fist after putting away an overhead to go up a break in the third set.
Djokovic became ragged, and his mood darkened when Bautista Agut levelled the match with a forehand off the netcord, the ball dropping dead on the world number one's side.
With the Spaniard making it a match, Djokovic flapped his arms at the capacity crowd in an effort to coax a show of support.
Djokovic is secure at the top of the rankings, whatever the result, but victory would lift Federer above Nadal to No 2, which was a sore point for the Spaniard when the Wimbledon seedings were announced and he was relegated to No 3.