Carter, who missed the 2024 autumn internationals and 2025 Six Nations because of injury, lasted only 24 seconds on his international return.
He was injured while making a tackle and after a lengthy stoppage, was taken off on a stretcher. James Ratti came on in his place, with both sides having to regroup.
Wales responded with a well-worked move that allowed Taulupe Faletau to provide a simple try-scoring pass to Thomas with Costelow converting.
Some more incisive attacking saw Adams burst down the left-hand side with his inside grubber kick almost finding scrum-half Hardy.
Wales had the early upper hand in the scrum, but their line-out was struggling and Japan capitalised on their first opportunity with a well-worked try for full-back Matsunga.
Scarlets midfield man Williams, who was back in Test rugby after an absence of almost two years, formed an eighth different Wales centre partnership in nine games this season.
Williams is more used to playing at inside centre but his defensive inexperience in the wider channel was exposed as Japan produced a fine attacking move, involving new cap Kippei Ishida before Matsunaga crossed.
Lee converted and it was 7-7 at the first water break after 20 minutes where Wales players used ice hats and towels to cool themselves.
Wales rallied and a clever kick from Hardy resulted in replacement wing Ichigo Nakakusu slapping the ball deliberately out of play to deny Adams a try-scoring opportunity and resulted in a penalty try and a yellow card.
Wales took advantage of their extra man after another fine Faletau break released the backs and wing Rogers scored in the corner.
The hosts responded with number eight Amato Fakatava denied by a last-ditch tackle by Ben Thomas.
The 40-minute first half lasted more than an hour with all the stoppages but Wales led by 12 points as both sets of players almost staggered off the field.
Either side of half-time Lake, Nicky Smith and Macleod, who was playing his first Test match in two-and-a-half years, gained valuable turnover penalties.
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