The 27-year old former European champion edged out Germany’s Tobias Wächter by a fraction of a second with Australia's Shane Perkins completing the podium.
Crampton, who won team sprint silver with Jason Kenny and Philip Hindes on Friday, had looked impressive throughout qualifying at the high altitude track in Mexico.
Laura Trott added silver in the omnium, behind world champion Sarah Hammer, as Great Britain finished third in the medal standings behind second-place Australia and leaders Germany.
Jess Varnish narrowly missed a medal in the women's sprint, while the madison pairing of Owain Doull and Jon Dibben also finished fourth.
World champion Becky James was fifth fastest in sprint qualifying but lost in straight races to China's Wai Sze Lee in the first round of knockouts.