Wright ended the match with a 103.52 average, over 15 points higher than his opponent, but Sherrock's perfection on the doubles made it a close and captivating contest.
Sherrock, a recent winner of the inaugural Women's World Matchplay, produced trademark finishes under pressure in front of the sell-out crowd at the AFAS Live, pinning the bull for a 73 checkout to lead 3-2, before landing a 120 finish to level at 4-4.
However, Wright kept his cool, with legs of 13 and 15 darts enough to prevent a last-leg shoot-out and book his place in round two where he will face Michael Smith in a repeat of January's World Championship final.
The opening night of the World Series showpiece saw a further seven first round ties take place, with the winners advancing to face one of the eight seeded players in Saturday's second round.
Dutch duo Danny Noppert and Dirk van Duijvenbode enjoyed victories on home soil against Simon Whitlock and Haupai Puha respectively.
Noppert raised the roof with a 170 checkout in his win over Whitlock to set up a meeting with reigning champion Jonny Clayton, while Van Duijvenbode came through a last-leg decider against New Zealander Puha and will next face Gary Anderson.
Vincent van der Voort was unable to make it a trio of Dutch successes as he went down 6-3 to Canada's Matt Campbell, whose next test will come against world number one Gerwyn Price.
Michael van Gerwen will begin his bid for a fifth World Series Finals title against Damon Heta, who ran out a 6-3 winner against Gordon Mathers in an all-Australian affair.
Leonard Gates enjoyed victory in his first TV appearance outside of USA, defeating Devon Petersen 6-4 to set up a clash with James Wade.
Gates' countryman Danny Baggish was narrowly denied in a last-leg decider by Ryan Joyce, who will now face top seed Dimitri Van den Bergh, while Dave Chisnall claimed a 6-3 win over Jamie Hughes and he will next meet Joe Cullen.
Saturday's second round winners will return for Finals Day on Sunday, when the quarter-finals will take place in the afternoon session before the semi-finals and final in the evening.
The tournament is being broadcast live on ITV3 & ITV4 in the UK, through the PDC's worldwide broadcast partners including DAZN and Viaplay, and on PDCTV (excluding subscribers based in the UK, Germany, Austria and Switzerland).
2022 Jack's World Series of Darts Finals
Schedule of Play
Friday September 16 (1900 local time, 1800 BST)
First Round x8
Ryan Joyce 6-5 Danny Baggish
Dave Chisnall 6-3 Jamie Hughes
Damon Heta 6-3 Gordon Mathers
Dirk van Duijvenbode 6-5 Haupai Puha
Leonard Gates 6-4 Devon Petersen
Peter Wright 6-4 Fallon Sherrock
Matt Campbell 6-3 Vincent van der Voort
Danny Noppert 6-4 Simon Whitlock
Saturday September 17 (1900 local time, 1800 BST)
Second Round x8
Gary Anderson v Dirk van Duijvenbode
James Wade v Leonard Gates
Joe Cullen v Dave Chisnall
Dimitri Van den Bergh v Ryan Joyce
Gerwyn Price v Matt Campbell
Michael van Gerwen v Damon Heta
Michael Smith v Peter Wright
Jonny Clayton v Danny Noppert
Sunday September 18
Afternoon Session (1300 local time, 1200 BST)
Evening Session (1900 local time, 1800 BST)
(1) Dimitri Van den Bergh v Danny Baggish/Ryan Joyce
(8) Gary Anderson v Haupai Puha/Dirk van Duijvenbode
(4) Michael van Gerwen v Gordon Mathers/Damon Heta
(5) Jonny Clayton v Simon Whitlock/Danny Noppert
(2) Gerwyn Price v Matt Campbell/Vincent van der Voort
(7) Joe Cullen v Jamie Hughes/Dave Chisnall
(3) Michael Smith v Fallon Sherrock/Peter Wright
(6) James Wade v Leonard Gates/Devon Petersen
First & Second Rounds: Best of 11 legs
Quarter-Finals: Best of 19 legs
Semi-Finals & Final: Best of 21 legs
Last 16: £7,500
Last 24: £5,000