Sherrock finished 131 to level the first set at two legs all before finishing 70 in three darts to take the set in the next leg. Suljovic won the next set to even it up at 1-1, but Sherrock hit back with the next two sets to knock the Austrian out of the tournament.
Sitting on 86 with a chance to win the match, she hit two single 18s and then a nerveless bull to win her second match of the championship and progress to the last 32. It appeared that she did not immediately appreciate the magnitude of what she had done - and for second time in four days.
When asked if she could win the tournament, Sherrock told Sky Sports: "Why not? I have won two games, I am just going to take each game as it comes but there is nothing to say that I can't. I am going to try.
"I have just proved that we [women] can beat anyone. I have beaten two of the best players in the world. If that doesn't show that women can play darts, I don't know what does."
She added: "I'm speechless. With everything that has been going on the last couple of days I have just been focusing on my finishing because I know that I can score.
"I'm still waiting for it all to sink in. I don't know how I'm going to sleep tonight. It's amazing, when that dart [at bull to win] went in it was a sigh of relief."