MATCH REPORT: Tigers pipped at the post in county cup competition
The Tigers fought back valiantly from a 2-0 deficit to level matters but were knocked out by a goal four minutes from time.
Twice in the first half Boston scored from corners but Holbeach gritted their teeth and with 10 minutes to go were back on level terms.
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Hide AdFirst Tommy Treacher pulled a goal back on the hour mark and then Josh Ford equalised in the 81st minute.
But the home side nicked it late on and will go through to meet Deeping in the semi-finals.
It was a fifth defeat on the trot for Holbeach.