ASH Pope scored the only goal of the evening as Christchurch edged past Bashley at the Glen Mex Stadium.
In both side's first game for more than a month, the visitors also ended the contest with 10 men following a red card shown to Ron Frost.
Almost 200 fans turned out for the Wessex Premier contest and almost saw Bashley take an early lead with both Cameron Beard and Conor Whiteley going close.
But the misses were punished when Pope fired across goal and into the corner to break the deadlock.
Harry McGrath struck the post after the restart, while Christchurch found themselves a man light for the final quarter of an hour with Frost shown his second yellow of the evening.
But Cherrett's side closed out victory to strengthen their grip on fifth spot.
Lymington Town continued their perfect record in the league, with Nathan Hurst's goal against Cowes Sports enough to make it nine wins from nine.
Poppies suffered a heavy 3-0 home defeat against AFC Portchester, while two Sami Makhloufi penalties helped Blackfield & Langley to the same score at Brockenhurst.
In Division One, a Chris Long brace and Conor Jevon strike earned New Milton Town a 3-2 win at fellow strugglers Downton.
Ringwood Town were also victorious, seeing off Petersfield Town 2-0 thanks to goals from Harrison Clarke and Ryan Osman.
In the League Cup, Jamie Beasley's goal secured Hamworthy United a quarter-final spot with a 1-0 victory at Verwood Town.
Tim Sills's men will host Whitchurch in the quarter-finals.
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