The 31-year-old, who had a previous career best of only 41, hit 11 sixes in reaching his hundred from just 34 balls – equalling the mark of the late Andrew Symonds for Kent in 2004.
It is the joint fourth-fastest century of all-time in T20 cricket, just four balls slower than the record set by West Indies great Chris Gayle in the Indian Premier League in 2013.
Abbott helped dig the hosts out of a hole at 94 for five as he dominated an unbroken sixth-wicket stand with Jordan Clark (29 off 17 balls).
Abbott hit 30 from the 17th over, bowled by his international team-mate Kane Richardson, and finished on 110 not out from 41 balls as Surrey posted a mammoth target of 223 for five.
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