Djokovic, the world No. 1, survived a strong challenge from eighth-seeded Juan Martin del Potro 7-5, 4-6, 7-6 (7-2), 6-7 (6-8), 6-3. Murray, ranked second, followed with a steady 6-7 (2-7), 6-4, 6-4, 6-3 victory over 24th-seeded Jerzy Janowicz.
Djokovic advances to his ninth final in the last 12 Grand Slam tournaments. He was a semifinalist in the other three. Included in that run is the 2011 Wimbledon title.
Murray was a finalist in last year's Wimbledon championships, losing to Roger Federer. He went on to defeat Federer for the Olympic gold medal at Wimbledon before getting his first major tournament title at the U.S. Open, beating Djokovic in the final. He is seeking to be the first British player since Fred Perry in 1936 to win Wimbledon.
Murray and Djokovic met in the final at this year's Australian Open, which Djokovic won in four sets, improving his lifetime record to 11-7 versus Murray. Murray beat Djokovic in the 2012 Olympics semifinals, their only meeting on a grass court.
Del Potro had dropped just two games on serve in the five matches leading up to the semifinal and Djokovic had trouble solving his serve. Djokovic, however, had his chances with 15 break-point opportunities.
He got his third break of the day to go up 5-3 in the fifth set and then held to close the match with his third match point chance. At 4 hours, 43 minutes, the match was the longest ever Wimbledon semifinal.
Neither Djokovic nor del Potro had dropped a set entering the semifinal, a string that broke for del Potro in the 12th game of the first set Friday. It was just the third time in the tournament del Potro had his serve broken.
Del Potro fought off four break points before holding and then broke Djokovic's serve at love in a game that was the difference in the second set. Neither managed a break chance in the third set but Djokovic won the final five points in the tiebreaker to take the set.
Each had a break midway through the fourth set and Djokovic was on the verge of ending the match at 6-4 in the tiebreaker. But del Potro came out on top at the end of a fantastic point and then won the next three points in forcing a fifth set.
Murray's win was more electric only because of the home crowd support. Janowicz dampened that some when he won the first four points of the first-set tiebreaker but Murray posted the match's first break in the first game of the second set to again enliven the fans as he evened the match.
Janowicz posted his lone break of the day and then held serve to go up 4-1 in the third set. Murray answered with a five-game winning streak to reach the verge of the finals.
He had to wait until officials, fearing darkness, closed the Center Court roof. After about 30 minutes, play resumed. Murray claimed a break in the third game and consolidated it at love -- winning the last two points with aces -- and held from there to get in position to close the match with his fifth break of the day.
Celebrity Breakups and divorces of 2014 [PHOTOS]