Carl Garner's reign as Clitheroe manager began with a 2-2 draw against Cheshire outfit Warrington Town.
The visitors shot into a two-goal lead with Chris Thompson and Alan Collins doing the damage.
But Clitheroe pulled a goal back on 29 minutes when Eastwood found Ashley Parillon, who made no mistake from 10 yards.
Jack Higgins levelled midway through the seco-nd half but the Blues were indebted to goalkeeper Zack Hibbert, who made some fine saves to keep the game level.
Clitheroe could have won it at the the end when Alan Coar fired into the side netting.
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