Peaty, who successfully defended his 50m and 100m breaststroke titles earlier in the week, teamed up with Luke Greenbank, James Guy and Duncan Scott to record a thrilling victory over the United States.
Scott's storming final freestyle leg helped the British quartet set a new European record of three minutes, 28.10 seconds.
After a solid backstroke leg from Greenbank, Peaty took over and unsurprisingly got Britain in front at the next change, but Guy was passed on the butterfly leg by America's Caeleb Dressel and Russia's Andrei Minakov.
Scott still trailed at the final turn by 0.84 secs but produced a strong finish to snatch victory, and his split of 46.14s would have broken the world record in a regular 100m freestyle.
In the women's race, the British quartet of Georgia Davies, Molly Renshaw, Alys Thomas and Freya Anderson could only finish eighth as the United States took gold in a new world record time of 3m 50.30s.
There was also disappointment for Max Litchfield in the men's 400m individual medley and Anna Hopkin in the 50m freestyle as both swimmers finished seventh.