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.
But despite an opening partnership of 108 from 59 between Daniel Bell-Drummond and Tawanda Muyeye, the total proved too much as a succession of wickets ended their hopes of victory.
Adam Finch smashed three sixes in the final over to earn Worcestershire a dramatic two-wicket victory over Yorkshire at New Road.
The 22-year-old was handed the tough test of needing 19 runs from the final over but the first ball from Matthew Fisher was slapped for a maximum before Finch finished things off with two sixes from back-to-back balls later in the over.
The home side were staring down the barrel of defeat when Fisher came to crease with his side on 145 for seven in the 18th over but claimed all-but one of the remaining 31 runs to snatch victory as Yorkshire still search for their first win.
Graham Clark fired a maiden T20 century as Durham claimed a dominant 10-wicket win over Northamptonshire at Wantage Road.
Durham had their tails up with the ball in hand with Nathan Sowter being the stand-out man, claiming his maiden five-wicket haul with figures of five for 15 as the hosts were restricted to 137 all out.
The Durham procession with the bat started straight away as they slogged 77 from the opening powerplay and Clark then rocketed to 102 off just 49 balls as the hosts reached their target with 6.4 overs to spare.
Birmingham maintained their winning start to the competition with a five-wicket victory over Leicestershire at the Uptonsteel County Ground.
Leicestershire’s miserable start to the campaign continued after they they limped their way to 166 for seven and a Bears side – which included Australian Glenn Maxwell for the first time – reached the target with 15 balls to spare, Maxwell getting 47 from 27.
Joe Clarke blasted 68 from 29 balls and Matt Montgomery notched a half century as Nottinghamshire kick-started their Blast campaign with a four-wicket victory over Derbyshire.
Half-centuries by Wayne Madsen (61) and Luis Reece (53) put Derbyshire in a good position as they looked for their first win at Trent Bridge in 10 years, but the home side fought back well to restrict them to 178 for six and eased home with 18 balls to spare with the bat.
James Vince hit an unbeaten 88 off 55 balls as holders Hampshire claimed a convincing eight wicket victory over Middlesex.
Pieter Malan’s 80 from 45 balls helped Middlesex to a total of 171, but in reply, Vince passed 5,000 T20 runs during his knock and put on an opening stand of 91 with Ben McDermott, cruising their way to victory with 13 balls to spare.
Timm Van Der Gugten and Ruaidhri Smith nudged Glamorgan to a tense two-wicket win over Severnside rivals Gloucestershire.
Gloucestershire set the visitors 162 for victory and they looked right on track through Colin Ingram and Kiran Carlson’s third-wicket stand of 69.
But the hosts clawed their way back in and Netherlands international Van der Gugten left it to the last over to smack a six and win the game with five balls to spare.