But Shields and Robson, who both narrowly missed out on playing a part in England’s World Cup campaign, crossed in the second half to seal the spoils.
Dai Young’s side bounced back from successive defeats in the first two games of the season, while Bath missed out on a losing bonus point despite the boot of Rhys Priestland.
Wasps struggled with discipline early on, conceding two penalties as Priestland got the scoring under way with a simple penalty.
The hosts broke through as Sione Vailanu gained ground with a powerful run, but Shields knocked on 10 metres from the line and Priestland punished them from the tee to make it 6-3.
Wasps struck at the perfect time, Robson drifting into space and offloading to Rowlands, who rumbled in from 15 metres out, Lima Sopoaga converting to earn a 13-9 half-time lead.
Seven minutes after the interval Bath stole a lineout and piled on the pressure, Mercer finishing off a long move from close range and Priestland adding the extras to hand the visitors a six-point lead.
Bath grasped the initiative as Priestland chalked up another three from in front of the posts, but it was from then on that the hosts were jolted into action.
Sopoaga orchestrated the move and Zach Kibirige did well to keep the Kiwi’s floated pass in play out wide, but Shields showed his strength to power over, helped by Vailanu.
It took just seven minutes for Wasps to do it again and Sopoaga came to the fore, with Tom Cruse finding space and advancing within metres of the line, offloading to Robson for the score.
Priestland turned the contest in the closing moments with a 70-metre kick that earned Bath territory, and he brought his side within five points on the final play.
Despite a clean break from Aled Brew, Wasps held on and Sopoaga kicked a penalty in the closing moments to deny Bath anything to show for their visit to the West Midlands.
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