SMART cookie Richard Gillespie continued to use his head to good effect as Bashley maintained the only unbeaten BGB Southern Premier home record.
The prolific marksman, who has just started a business masters' degree, nodded home a second-half clincher to seal a deserved sixth league win of the season.
Gillespie converted Justin Keeler's precision cross after the pair had combined to open the scoring as Bash threatened a first-half goal fest.
But Keeler's clinically-taken 22nd-minute effort was all the New Forest outfit had to show for their dominance and they were almost made to pay for their profligacy after the break.
Former Torquay defender Matt Villis restored parity with an unopposed diving header, the Devonians profiting as the hosts' took a mid-match siesta.
But Gillespie, who turns 23 on Wednesday, quickly responded as Steve Riley's troops heeded their wake-up call to remain firmly in the hunt for a second successive promotion.
Bash's victory, which should have been more emphatic, keeps them in sixth place in a highly competitive division where the top 11 are separated by just seven points.
"It was a pleasing win," said Gillespie after notching his eighth goal of the season. "I thought the scoreline flattered them. They did okay towards the end and started getting the ball forward, but our passing game was very good and I thought we had a little bit more on them."
Gillespie was a constant menace as Bash mounted a wave of first-half attacks. But some wayward finishing, coupled with one excellent save by Tivvy goalkeeper Ray Johnston to deny Keeler, kept the visitors interested.
"We had a lot of possession in the first half," said Gillespie. "We created chances but a lot of them were only half chances.
"As the games go on, we seem to be getting used to the new level and how these teams play. Hopefully, we will start to create more chances and the recent signs are pretty good."
Although Gillespie turned provider for Bash's opener, he admitted his assist had been aimed at Jeremy Tarr: "I saw Jeremy in the box but didn't see Justin behind him. Jeremy stepped over the ball and, with his technique, Justin doesn't miss from eight yards, not an open goal anyway!"
Boasting former Rangers and England under-21 captain Chris Vinnicombe among their ranks, Tivvy's two best chances of the opening period fell to Chris Young and Lee Groves, with both narrowly off target.
But after Johnston had acrobatically saved Gillespie's 51st-minute header, Villis arrived on the scene to convert Vinnicombe's free kick to make it 1-1.
And although Johnston again denied Gillespie with another point-blank stop, the striker had the last laugh after Keeler had returned the loose ball into the six-yard box.
"Jeremy Tarr put me through with a great ball and I was annoyed with myself for not scoring the first time," said Gillespie. "I nicked it to the side of the keeper and he stuck his hand out at the last second. But, within seconds, Justin whipped in a really nice cross and I didn't have to do too much except just get my head on it."
Bashley: Elm, Hill, Ferrett, Castle, Gazzard, Keeping, Wakefield, Davis, Tarr, Gillespie, Keeler. Unused subs: Blackmore, Burden, Tanner, Williams, Harper (g/k).
Tiverton Town: Johnston, Groves, Vinnicombe, Villis, Rudge, Gardner, Sczabo, Gould, Young, Knighton, Wyatt. Unused sub: Clarke.
Booked: Johnston, Groves, Villis, Rudge, Young.
Attendance: 319.
Referee: Will Bull (Winchester).
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