Ben Jackett took 4-33 and Jono Hall 3-25 although opener Liam Dudding was 0-28 off 10.
Cornwall manager Neil Jackett was just happy to have made the cut despite losing home advantage.
"We didn't play as well as our last game but we posted a good total and defended it well," Jackett said.
At Ongaonga Domain, a depleted CHB succumbed to a three-wicket, bonus-point defeat to Taradale CC who are out of the playoffs.
The hosts were 206 all out with an over to spare with Paul Hindmarch (62 runs) and Henry Hunter (43) the key batsmen.
Callum Hewetson took 3-29 and Eddie Torr 2-37 before Taradale eclipsed the total by one run in 45.2 overs.
Hewetson again delivered with 51 runs while Ajaz Patel was 32 not out.
CHB coach Colin Schaw took 4-54 and son Angus Schaw 2-28.
CHB manager Mike Lewis said seven first-team players were missing but admitted the visitors deserved their win.
"We can be philosophical on the day to say we've got as much a chance as Tech of winning," Lewis said, expecting to field a full-strength side.
Only Havelock kept to the script, beating The Station Napier Old Boys' Marist (NOBM) by eight wickets at home with a bonus point to boot.
NOBM mustered 132 in 35.2 overs with Llorne Howell scoring 35 and S Gibson 25 and wicketkeeper Josh O'Brien contributing 31.
Kurt Richards took 3-33 while Jared Priest and Stu McVeigh claimed two scalps each.
In reply, the villagers strolled across the park with 134-2 in 19.2 overs.
Opener James Taylor scored 47 runs and Graeme Tryon was unbeaten on 42.
"I don't mind who we play - we want a home semifinal," Havelock captain Todd Astill said before the CHB result.
Astill got his wish.
