Carthy is one of only two men to be within a minute of race leader Primoz Roglic, with Richard Carapaz 39 seconds adrift in second place.
Roglic retook the overall lead on the stage with a dramatic time trial win. Jumbo-Visma’s Roglic, from Slovenia, snatched the stage victory over the 33km route from Muros to Mirador de Ezaro by one second from America’s Will Barta.
Carapaz, the race leader after stage 12, finished seventh, and the Ineos Grenadiers rider now trails Roglic by 39 seconds.
“It’s beautiful, eh? It’s a long time since I won a time trial. I felt strong, surprisingly. I thought I would suffer a lot more,” Roglic told Eurosport.
Carthy, from Fulwood, made sure he remained in contention, the EF Pro Cycling rider finishing fourth to lie third overall, 47 seconds down.
Earlier, race organisers announced that all riders and other members of the ‘race bubble’ were tested for coronavirus, for a fourth time, on their rest day.
All 681 tests came back negative.