Despite dominating possession for long periods of the match, the home side just could not break through the Chiefs defence as they slumped to an eighth straight Aviva Premiership defeat.
A game that was played in wet conditions never really caught fire with tryscoring opportunities rare - but this will matter little to Rob Baxter's resilient Exeter.
The hosts replied with four penalties by Nick Robinson but this is another damaging blow to their morale.
Wasps came into this game desperate for a result given their recent poor form, which has dragged them into a potential relegation dogfight with Newcastle.
Exeter came into the game off the back of completing a league double over Leicester and are still in the hunt for a Heineken Cup place.
The hosts gave a first start to Wales international Tom Prydie on the wing while recent signing Paul Emerick was named amongst the replacements.
And they had the first points in the third minute when Robinson slotted a penalty after the Chiefs had been pinged for offside.
The fly-half then should have doubled his side's advantage soon after with a straightforward attempt but he skewed his kick wide of the left hand post.
It was a strong start from Wasps who dominated the early possession with only a couple of wild off-loads preventing them from making any more headway.
But the Chiefs drew level from their first real attack after Richard Baxter was stopped a few metres short as Mieres made no mistake with the resulting penalty.
But the Argentine then got lucky when his clearance was charged down by Wasps captain Marco Wentzel but the ball went beyond the dead ball line before Nic Berry could reach it.
Mieres then kicked the visitors in front with a superb penalty from the half-way line that sailed between the posts.
Wasps came close to squaring it up again as Elliot Daly's long-range penalty dropped wide as conditions continued to worsen.
This obviously made handling increasingly difficult but there was nothing wrong with Mieres' kicking as his third penalty gave the Chiefs a 9-3 lead at half-time.
They extended that lead to nine points early in the second half with Mieres again lethal from long range - despite him now kicking against the wind.
Robinson managed to pull three points back soon after as the Chiefs were, not for the first time, penalised for an offence in the scrum.
But after Richard Birkett was penalised for not rolling away from a tackle, Mieres punished Wasps again with another clinical kick to stretch the lead to 15-6.
Robinson then kicked his third penalty to reduce the deficit once more after Gonzalo Camacho's fumble had put his team into trouble close to their try-line.
A superb burst by Billy Vunipola through the middle took Wasps within inches of the Exeter line and the visitors were eventually caught offside.
This gave Robinson the simplest of penalties under the posts and he reduced the gap to three points with 12 minutes still to play.
It was all Wasps in the closing stages and they were denied when Robinson broke through before passing to Emerick, who was superbly tackled into touch by two Chiefs players.
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