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The former Ipswich striker scored twice in Wednesday's 4-0 win over Tonbridge Angels and carried on where he left off with a second-half strike.
Following a goalless first half in which Gary Alexander missed a penalty, Nicky Adams put Sean O'Driscoll's side ahead after the break and Jonte Smith doubled the lead.
Bromley pulled one back but Clarke grabbed Crawley's third when he tucked away Adams' pass, before the non-leaguers struck again 10 minutes from the end.
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