Defending champion Andy Murray, who was hampered by a hip injury, suffered a shock quarter-final exit to American Sam Querrey at Wimbledon.
Murray's hopes of becoming the first Briton to retain a grand slam title since Fred Perry in 1936 evaporated as he hobbled helplessly to a 3-6 6-4 6-7 6-1 6-1 defeat on a stunned centre court.
Querrey reached the first grand slam semi-final of his career and will meet Croatian Marin Cilic, who also needed five sets to end 16th-seeded Luxembourger Gilles Muller's run at the championships.
Muller took the first set but Cilic recovered to win 3-6 7-6 7-5 5-7 6-1 after three hours and 30 minutes of play on court one.
Second seed Djokovic, who needed to win the title to return to the top of the rankings, was 7-6 2-0 down when he shook Berdych's hand to concede defeat.
Seven-time champion roger Federer needed just under two hours to see off Canadian Milos Raonic 6-4 6-2 7-6 to set up a final four meeting with 11th seed Berdych.
Third seed Federer was in top form as he recorded 46 winners on his way to a 12th semi-final at the championships.