The 25-year-old became the first woman to win a match in the tournament when beating Ted Evetts before following it up by stunning world number 11 Mensur Suljovic.
But Dobey proved too strong, fighting back from 2-1 down to silence the crowd and set up a clash with Glen Durrant in the fourth round.
Sherrock, who was cheered to the rafters throughout, twice led by a set, going 1-0 and then 2-1 up in the early stages, helped by some superb finishing.
Indeed, she hit 50 per cent of her doubles in the match overall, compared to Dobey’s 36 per cent.
Dobey made his scoring count, however, averaging 101.09 to Sherrock’s 90.45, while he also hit eight 180s compared to Dobey’s 11.
The 29-year-old struggled to hit his doubles in the early stages, with the crowd firmly in his opponent’s corner, but he found his stride as the match wore on before sealing victory with a 94 checkout.
Sherrock’s achievements have made her the breakout star of these championships, regardless of what happens in the rest of the tournament.
And she admitted after Friday’s match she had not envisaged her run to the last 32.
“I enjoyed myself so much,” the mother of one told Sky Sports.
“I didn’t think this was ever possible.
“This is amazing, this whole experience has been unbelievable.”
On her loss to Dobey, Sherrock added: “Chris played so well. Unfortunately it wasn’t to be but I can’t take it away from him.
“Hopefully I get to be back here next year but I’ve got the Ladies World Championship next week so let’s see where I go from there.”
Tennis great Billie Jean King has followed Sherrock’s run and hailed her as an inspiration.
She tweeted: “While her run at the #WorldDartsChampionship is over, @Fsherrock has inspired millions. Her talent & grace under pressure will take her far. She is the 1st woman in history to win matches in the championship & I look forward to following her career for years to come. #Gamechanger”