The 31-year-old, who had been around the top of the leaderboard all weekend having led by three shots after the first round, finally ended his wait for a maiden PGA Tour title at El Camaleon Golf Club.
Kizzire posted four birdies in a bogey-free round to set the clubhouse lead on 19-under for the tournament and watched as fellow American Fowler also carded a 67 after missing a final-hole birdie required to take it to a play-off.
Afterwards, world number 236 Kizzire said: "It was pretty nerve-wracking but it felt good. I've been in tough spots before and drew from that.
"It means a lot, I'm pretty emotional right now and was glad to get it done, Rickie made me work hard."
Inclement weather across the weekend meant 13 players had to play 36 holes on Sunday as Korean Si Woo Kim hit back from a double bogey on the back nine to fire five successive birdies which was enough to claim third place thanks to a six-under-par 65.
Charles Howell III finished in share for fourth place alongside Martin Piller on 14 under after he carded back-to-back 66s.