The 25-year-old, who became the first woman to win a match at the PDC World Championship in December – defeating both Ted Evetts and Mensur Suljovic – was bidding to become the first challenger to win at the tournament.
She stayed in the match throughout and had the crowd on their feet in leg seven with three triple-figure visits before a superb 92 checkout with bull, six and double 18.
Sherrock threw for the match in the final leg but was broken by the three-time BDO world champion and had to settle for a draw.
"I've loved every minute of it. I'm so happy that I get to play again on the big stage. It's been incredible," she told Sky Sports afterwards.
"I'm speechless because everyone's come and it's amazing. I just thank everyone that's here supporting. I'm so grateful."
Discussing what comes next for her, Sherrock added: "I'm getting opportunities opening up all the time, so obviously I'm excited to see what 2020 holds for me.
"I can't wait for everything that's coming and I'm just loving this at the moment."
Durrant missed a string of doubles throughout the match but finally found his range in the last leg to break Sherrock's throw and earn himself a point.
The 49-year-old paid tribute to his opponent, who had the vociferous backing of the Nottingham crowd.
"All credit goes to Fallon," he told Sky Sports. "She's just had the most amazing couple of months. That just cemented that.
"To play in the Premier League... that was the toughest game I've ever had. Playing Fallon Sherrock on that stage is a lot harder than maybe I anticipated. I'm very lucky to get the draw."
Defending champion Michael Van Gerwen is the only player with maximum points from the opening two weeks and he tops the table following an exceptional display to defeat Daryl Gurney.
Van Gerwen claimed a 7-1 win over Gurney with a 105 average, as well as hitting seven out of 11 on the doubles. Gurney on the other hand is down in last place with no points after a crushing defeat.
Rob Cross got his first win with a dramatic 7-5 success against Nathan Aspinall. "The Asp" twice squandered a break of the darts, in leg three and leg seven, but on each occasion failed to stamp his authority and allowed his opponent to stay in the match.
Cross saved his throw with an incredible dart at double 16 from well wide of the oche in the penultimate leg before winning the match with a break of throw at the same double.
Gerwyn Price, who drew with Cross during week one in Aberdeen, staged a remarkable comeback to draw again and deny Michael Smith what seemed like a certain victory.
The 2018 Premier League runner-up lived up to his "Bully Boy" moniker early on by storming into a 6-2 lead. He missed the seventh dart of a possible nine-darter en route to hitting two 10-dart legs and averaging, at one stage, 120.
However, Price displayed the never-say-die attitude for which he is renowned, reeling off the final four legs to snatch a point.
Peter Wright got off the mark with a hard-fought draw against Gary Anderson.
The world champion injured himself jumping on the stage but he hit a brilliant last leg to snatch a draw from Anderson who was left on a finish and ready to inflict back-to-back defeats on his fellow Scot.