CITY were denied a second National League South win in four days when Weston scored an equaliser three minutes from time at Winterstoke Park
After falling behind at the start of the second half City to an Ollie Barnes header, the looked to have turned the game round with two quick goals by Arran Pugh and Cody Cooke.
But with time running out, a visibly tiring City side could not see the game out with Scott Wilson firing home a fine equaliser into the corner of Martin Rice's goal.
It was tough on a Truro side, who gave a debut to new signing Jamie Richards in central defence in place of the suspended Rob Farkins, in the only change from the side that started Saturday's 2-0 home win over St Albans City.
And City boss Steve Tully said: "We just ran out of legs. Of course its disappointing we could not hold out, but I am delighted we kept our run going."
After a pretty uneventful first half, the home side who started the match bottom of the table, took the lead when Barnes headed home from a corner.
Pugh then got City level after 78 minutes, with a good finish from just inside the box following a corner and man of the match Cooke tapped in at the far post two minutes later from substitute Les Afful's cross.
However, City could not hold out and stay 16th in the table with ten points from their opening ten matches.
CITY: Rice; Mitchell, Pugh, Richards, Riley-Lowe; White (Brett); Green, Cooke, Dawson; Wright (Afful 72), Duff (Vassell 64). Subs (not used); Yeoman, Ash.
Yellow cards: Green, Pugh.
Goals: Paull (48) 1-0, Pugh (78), Cook (80) 1-2, Wilson (87) 2-2.
Referee: Dan Cook.
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