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Will Evans headed inches wide from an Oli Irow cross after 18 minutes as Argyle tried to up the pressure against a well-organised defence.
Xavier Amaechi skimmed the bar with a 20-yard free-kick on 30 minutes while visiting goalkeeper Redman Evans had to punch Harvey White’s inswinging 37th-minute corner off the line.
Amaechi’s corner caused panic in the Church box at the start of the second half with a frantic goal-line clearance during a goalmouth scramble keeping the score level.
Will Evans finally broke the deadlock after 50 minutes, winning the ball from Jessy Bavanganga before driving a low angled shot into the far corner.
Redman Evans made a brilliant diving save to deny Bim Pepple from close range on 62 minutes but Will Evans claimed the final touch as substitute Ronan Curtis’ 69th-minute shot was blocked on the line then bundled in by the forward.
Michael Baidoo first-timed fellow sub Jared Rendle’s 78th-minute cross home and then Curtis latched on to White’s incisive through ball to make it 4-0 with 10 minutes left.