Watched by a Royal Box crammed with sports and movie A-listers - David Beckham, Rod Laver, Gary Player, Jude Law, Damian Lewis - Djokovic swept through the first set with breaks in the second and eighth games.
Nadal carried that momentum with him and broke again two games later before serving out the set and levelling the match up after nearly 90 minutes on court.
The champion then took command in the fourth set, cutting out the loose groundstrokes and picking up points with adventurous serve-and-volley attacks and after breaking for a 2-1 lead he never looked back.
Nadal won the first point with a stunning shot at the net to beat his opponent down the line, but Federer came back, eventually winning the tiebreak 7-3 to take the opening set.
"I am sad for the loss because for me it was another opportunity", he said. Just one of those initial 14 points came via his own victor; 10 resulted from Bautista Agut's unforced errors.
Defending his backhand nicely, Roger avoided slices and lengthy exchanges to hit in full throttle, taming his shots nicely and overpowering Nadal in sets three and four to book the place in the final against Novak Djokovic, the first since those two title clashes in 2014 and 2015.
Federer has held on to his serve and with it he makes life hard for Nadal.
Remarkably the Serb's 6-2, 4-6, 6-3, 6-2 success was the 12th victory in his last 13 grand slam semi-finals and he is now one win away from his fifth title at Wimbledon and 16th grand slam singles crown as he resumes his great rivalry with the Swiss.
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"He was not really overwhelmed, so to say, with the stadium and with the occasion".
Djokovic was broken once in the second set, allowing Bautista Agut to even the score.
"He played really well". "First set, he was still probably managing his nerves and he made some uncharacteristic unforced errors".
After a flat forehand return victor off a 107 miles per hour serve on the very first point, Bautista Agut certainly did lose his way for a bit. It's their 14th match at a major; Nadal leads 10-3. Only one victor from here, right? You can find the Novak Djokovic v Roberto Bautista Agut live streaming options along with its preview, head to head and tips here for a match that will begin at 1 pm local time (12 noon GMT).
But the second set saw a shift.
No, largely because Djokovic rediscovered his best abilities.
Between them, come Sunday, they will have won the past 11 major titles. He double-faulted on his first set point but converted the second with a volley victor that clipped the net cord.
In the third, Djokovic broke for a 4-2 lead and then saved two break points in the next game - the second with a backhand victor down the line after a 45-stroke rally.