Beckett has scored nine goals in 12 games for Gainsborough
Gainsborough Trinity picked up their first away win in five games on Saturday, with a 2-0 victory at Hinckley United in Blue Square North.
Ashley Burbeary's deflected 23rd-minute effort put Trinity ahead.
They doubled their lead in the 65th minute when Hinckley goalkeeper Chris McKenzie allowed Luke Beckett's shot to go through his legs.
Trinity's Adam Sollitt told BBC Radio Lincolnshire: "We were due that win and it was a good one, we worked well."
Boston United have dropped into the Unibond Premier Division relegation zone after their match at Bradford Park Avenue was postponed and their next league opponents Witton Albion beat Buxton.
In the Unibond First Division South, Sean Cann's 90th-minute goal gave Lincoln United their sixth consecutive away victory as they beat Carlton Town 1-0.
Stamford stretched their unbeaten league run to 18 games with a goalless draw at Loughborough Dynamo, while the match between Grantham Town and Spalding United was postponed because of a frozen pitch at the Meres.
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