Anderson had a break and set point chance at 5-4, but Isner fired down a gutsy 129mph unreturned second serve to keep himself in contention.
That inconsistency was eliminated in an absorbing final set before Anderson produced a moment of magic. The former Bulldog broke right back to even the set once again.
An Isner ace fittingly concluded the 12 games in the first, before Anderson recovered from a mini-break down to take a one-set lead after an hour and three minutes.
At Wimbledon, there are no fifth-set tiebreaks, a rule with which Isner is extremely familiar, so one of the players was going to have to break the other's serve at least once in order to reach the final.
Isner would like the US President, a serious tennis fan, to be in the Centre Court crowd as his guest for what promises to be another battle of big serves against Kevin Anderson. It was a drama filled set that went back-and-forth, similar to the third set.
Significant reason Kate Middleton has always worn white at christenings
While Kate cradled the littlest royal, Prince William guided Prince George, 4 , and Princess Charlotte, 3 , inside. The little prince wore the same gown his older siblings wore to their christenings and continued the tradition.
Isner and Raonic entered Wednesday night's quarter-final as the two leading players for aces in the tournament at 135 and 117 respectively.
The reason the match went on for so long comes down to one of Wimbledon's quirks - a five-set match can not end on a tiebreaker, a tradition shared at the French Open and the Australian Open.
At 24-24 Anderson took a tumble but managed to get to his feet and hit a left-handed shot inside the baseline, taking the point for 0-30.
It's not the first time that Isner has played to a marathon match - back in 2010, he defeated Nicolas Mahut 6-4, 3-6, 6-7 (7), 7-6 (7), 70-68 in the first round at Wimbledon in a match that lasted over 11 hours and was played over three days.
Isner's semifinal match is scheduled for 7 am Dallas time on Friday and can be watched on ESPN.