Let's not forget the "opening act" with the great Steve Allen.
Since you brought it up,
mi amigo:
Allen, the original host, had only three years as host (and for the last two years, Ernie Kovacs was host for two of the five nights.
Jack Paar, who succeeded Allen in 1957, did five years.
And it was only from Carson on forward that it was called "The Tonight Show". Under Allen and Paar it was simply titled "Tonight" (reportedly because the late Sylvester "Pat" Weaver, then head of NBC programming, wanted it to be a counterpoint in viewers' minds to the "Today" show which debuted in 1952). There was a six month period in 1957, between the Allen/Kovacs years and Paar, when it went more in a news direction and was titled "Tonight! America After Dark", hosted first by Jack Lescoulie and for the last month by Al "Jazzbo" Collins.
Incidentally, when doublechecking the timeline on Wikipedia, it appears that someone actually tallied up the number of shows under each host. There were approximately 2,000 shows pre-Carson (Allen, Kovacs, and Paar combined). If you combine both of Jay Leno's stints you get 4,610 shows, which puts Carson in second place with 4,531. This is largely, it is explained, by Carson's cutting back to three new shows per week in the 1980s, and the number of guest hosted shows during Carson's years. Leno did five new shows per week and also did not use guest hosts. Leno's total does not include the shows he did as permanent guest host during Carson's last five years.
Fallon has done 2,229 shows and poor Conan O'Brien only got to do 146 before NBC pulled Jay back from that disaster of a 10:00pm show in 2010.