The Division One side more than matched last season's Premier Division winners in a cagey first-half.
And they were in dreamland just before the hour mark when Tom Morgan headed them in front.
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But Lewis Walmsley restored parity on 77 minutes and then skipper put Thornton in the lead on 86 minutes.
Walmsley then completed the turnaround in injury time to seal a 3-1 win.
In League action, both Hesketh Bank and Rossendale kept up their fights for promotion from Division One with midweek wins.
Bank travelled to Haslingden St Mary's and goals from Dan Birkby and Joe Smyth-Ferguson earned them a 2-0 win.
Rossendale made light work of Horwich St Mary's racing into a three goal lead inside 30 minutes through Mickey Saunders and a Tom Hulme double.
Mason Greeley pulled one back but Tom Hartley and Scott Wylie added further goals in a 5-1 success.
In Division Two, Cameron Laurie grabbed the only goal in Charnock Richard's 1-0 over Astley and Buckshaw.
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