On his 18th birthday, Dwyer was offered his first professional contract with the club by manager Jimmy Scoular, earning £20 per week. With Cardiff struggling in the Second Division during the 1972–73 season, Dwyer became increasingly involved in the first team as Scoular attempted to improve the side's fortunes. On 7 October 1972, Scoular dropped David Carver from the side and handed Dwyer his professional debut against Leyton Orient. Playing as a right-back, he helped the side record a goalless draw, having been reduced to ten men when Alan Foggon had been sent off after 30 minutes. Dwyer remained in the first team for the remainder of the season and was ever present for the side in all competitions following his debut. He made 40 appearances during the season, helping the side narrowly avoid relegation with a 1–1 draw against Sunderland in the final match of the campaign. Despite the team's disappointing league form, Dwyer ended the season by winning his first senior trophy as Cardiff defeated Bangor City 5–0 in the final of the Welsh Cup.