Dobromyslova didn't play up to her usual standards but neither did Sharon Prins and as a result, she came through in a 2-0 victory.
Prins kicked off proceedings claiming the first leg but from there Dobromyslova took the set with legs ranging from 19 to 26 darts.
The next set went to a decider but the multiple World Champion saved her best leg for the end of the match hitting an 18 darter when it mattered to move through to the Quarter-Finals.
Veenstra also moved through with victory over Justin Hood who had impressed in his first round tie. 'Flyers' flew into the lead winning the first two legs but Hood forced a decider which Veenstra claimed.
He followed that up with finishes of 127 and 145 to claim the second set. Hood returned strongly after the break, he added to his six 180's and claimed the third set but this revival didn't last long with Veenstra taking the match and setting up a tie with David Evans next.
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David Evans (83.65) 3-2 (88.26) Nick Fullwell (R2)
Nick Kenny (89.02) 2-3 (88.15) Dennie Olde Kalter (R2)
Anastasia Dobromyslova (64.51) 2-0 (62.35) Sharon Prins (R1 women)
Richard Veenstra (86.31) 3-1 (90.22) Justin Hood (R2)
Gary Robson v Ben Hazel (R2)
Lisa Ashton v Paula Jacklin (R1)
Scott Mitchell v Leighton Bennett (R2)
Ryan Hogarth v Thibault Tricole (R2)
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