A brilliant opening stand of 166 between Sam Frankland and Tim Jackson helped the Bradford League champions pass Thornes’ 40-over 197-7 total with surprising ease as they got home with 4.1 overs to spare.
Frankland was the only Woodlands batsmen to be dismissed, but not before he had made 88, including 11 fours and three sixes.
Jackson remained to see the job through to the end, finishing not out on 84 having hit 13 boundaries while Liam Collins contributed 14no.
Wicketkeeper Joe Billings (67) and Matty Taylor (33no) were the main contributors for Yorkshire Premier League South side Thornes after they had elected to bat first.
But the Wakefield batsmen never truly got on top of the Woodlands bowling with Kez Ahmed taking 2-21, Muhammad Bilal 2-29 and Tom Clee 2-36.
In the next round Woodlands will come up against a player who wrote his name into Ashes folklore in 2005, the Richmondshire captain Gary Pratt.
He is best remembered for fielding as a substitute for England in the Trent Bridge Test and running out Australian captain Ricky Ponting.
Woodlands will visit their North Yorkshire South Durham League opponents on Sunday, May 29.