Dwyer missed the start of the 1976–77 season after breaking his ankle in a baseball match days before the club's first match of the campaign against Swiss side Servette in the Cup Winners' Cup. He had continued to play baseball alongside his football career, concealing the fact from the staff at Cardiff, and hid the cause of the injury by claiming he had fallen down the stairs at his home. He returned to the side in late September, in a goalless draw with Millwall. The team travelled to Georgia ahead for Dwyer's next appearance where they suffered a 3–0 defeat to Dinamo Tbilisi in a match that was attended by 100,000 spectators. Upon his return, Dwyer found himself playing in his more usual role in defence rather than in midfield. Cardiff again struggled in the Second Division but avoided relegation on the final day of the season, after drawing 1–1 with Carlisle United.