Murray, the world No. 2 and seeking to become the first British men's player to win the Wimbledon singles title since Fred Perry in 1936, roared back from the two-set deficit for a 4-6, 3-6, 6-1, 6-4, 7-5 win over unseeded Fernando Verdasco in about 3 1/2 hours.
Djokovic, the No. 1-ranked player in the world, ousted No. 7-seeded Tomas Berdych 7-6 (7-5), 6-4, 6-3 just moments after Del Potro, seeded eighth, finished off a 6-2, 6-4, 7-6 (7-5) win over fourth-seeded David Ferrer. Djokovic and del Potro will meet in one of Friday's semifinals.
Murray, who lost the Wimbledon final to Roger Federer a year ago, takes on 24th-seeded Janowicz in the other semi. Janowicz defeated his Polish countryman Lukasz Kubot 7-5, 6-4, 6-4 in his quarterfinal.
Murray had the lone dramatic match of the day, handing Verdasco a decisive break in the first set with a double fault and then having trouble holding the advantage of an early second-set break. He allowed Verdasco only four break chances the rest of the way, saving all of them. He had a pair of third-set breaks and used another in the seventh game of the fourth set to even the match.
Both players held until the 11th game, when Murray recorded his fifth break of the day. He held at love to close the match.
He'll go against Janowicz for the third time in their careers, with each payer winning once. Janowicz fired off 30 aces against Kubot and didn't allow Kubot to convert any of his six break chances while getting one break late in each set.
Djokovic came back from a two-break deficit in the second set and won six of seven games to take the set and command of the match. Djokovic cashed in the only break opportunity of the third set and earned his fourth consecutive trip to the Wimbledon semifinals.
Djokovic allowed Berdych only two break opportunities -- those allowed Berdych to take the second-set lead -- while finishing with four breaks himself. Djokovic won more than 70 percent of the points on serve.
Del Potro seemed to injure his knee in the first game against Ferrer but relied on a superior serving game to gain his third Grand Slam semifinal. He won the U.S. Open in 2009 and was a semifinalist at the French Open that year.
To get to the 2013 Wimbledon semis del Potro saved the only two break points he faced and won three-quarters of the points when serving. Del Potro had three breaks but there were no break chances in the third set. Del Potro, however, closed the match with two of his 42 winners.
Djokovic, seeking a second Wimbledon title, is 8-3 all-time versus del Potro, although del Potro won their most recent meeting.