Fresh from a 2-1 home win over the Cestrians before Christmas, the Pilgrims found their hosts a tougher nut to crack on this occasion.
Chester's goals were scored by Josh Maris and Sam Bradley.
Boston (3-4-2-1): Jake Lovelace; Oskar Rajski (Lucas Stubbs 63), Owen Sheriff, Taylor Jaine; JJ Ward, Han Stevens, Kyle Featherstone (Patrik Bad 62), Josh Doran (Jake Higginbottom 70); Jack Waddington, Rueben Fogg; Flynn Slater.