Resuming after a severely rain-shortened second day in the relatively comfortable position of 169 for two in Barbados yesterday, the hosts lost Darren Bravo early on and Shivnarine Chanderpaul on the stroke of the interval to the persevering left-arm seamer.
In between, Tim Southee accounted for Kirk Edwards to stall the Caribbean side's quest for a potentially decisive first innings lead.
Twice he drove Wagner for boundaries just out of the reach of the close-in fielders. He attempted the shot once too often though and a thick outside edge was well held by Kane Williamson at gully to send Bravo back for 24.
Edwards was also restrained by the much more disciplined bowling, but reached his second consecutive half-century with a beautifully-timed cover-driven boundary.
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But like Bravo, he fell looking to go to his favourite area, an attempted on-side flick taking a leading edge for Hamish Rutherford to complete a very good catch running back at mid-on.
However the combative South African-born seamer had the last laugh when Chanderpaul, on 15, gloved a leg-side delivery for wicketkeeper B.J. Watling to take a good catch tumbling to his right.
Debutant Jason Holder is expected to partner Ramdin (20 not out) on the resumption after the interval with the onus on the West Indies skipper to shepherd the lower half of a batting order
The lower batsmen have a look of vulnerability following the decision to omit Jermaine Blackwood and play Holder despite the Jamaican's score of 63 on his debut in the second Test in Trinidad.