The eighth-seeded pair won 7-6 (7/2), 6-4, 3-6, 4-6, 13-12 (7/2) in four hours and 29 minutes.
The third round match was suspended due to bad light on Monday and resumed Tuesday on the 1,750-seater Court 12 show court.
The All England Club introduced a final set tie-break this year as a means of eradicating marathon matches.
In 2018, Kevin Anderson defeated John Isner in the men's semi-finals in the second-longest match ever at the Slams, at six hours and 36 minutes.
The final set, which alone lasted for two hours and 50 minutes, was only decided at 26-24.
The second semi-final, in which Novak Djokovic defeated Rafael Nadal 10-8 in the final set, took five hours and 15 minutes.