Alexander Dalziel Downes was born in Emerald Hill, Victoria, Australia, on 2 February 1868, the son of Thomas Nichol Downes, a plumber, and his wife, Isabella Livingstone. The family emigrated to Dunedin, New Zealand, about 1870. Nothing is known of Alex Downes's education, but in 1882 he began work as a brass-finisher for A. & T. Burt.
Downes first came to prominence as a rugby player. He was one of Otago's greatest centre three-quarters and was known for his ability to drop-kick goals. He was associated with the formation of the Alhambra Rugby Football Club in 1884, appearing in their inaugural senior team of 1887 and representing the club until 1893. He represented Otago on 13 occasions between 1887 and 1893, and the South Island in 1888 against A. E. Stoddart's English team. In 1897 he was made a life member of the Alhambra Rugby Football Club.
However, it was as a cricketer that Downes was to find fame. As a youth playing for the Carlton Cricket Club he was selected for the local north versus south match. In the following season, 1886–87, he joined the Grange Cricket Club. Selected for Otago in January 1888, he was an immediate success, taking five wickets for 34 runs in Canterbury's first innings. From 1890–91 he formed a formidable partnership with Arthur Fisher for Otago, and later New Zealand.
By February 1894 Downes was being described as the best bowler in New Zealand. He bowled right-arm with a great variety of pace, a big off-break and a fine length. Downes's bowling record was nothing short of remarkable, especially in Dunedin. Of the 28 matches that he played there for Otago he took 10 or more wickets in a match on 13 occasions. His career bests for an innings were 8 for 35 against Canterbury in 1891–92 and 14 for 103 in a match against Hawke's Bay in 1893–94. He also recorded the unique feat in New Zealand first-class cricket of taking four wickets in four consecutive balls against Auckland in January 1894 on Carisbrook Ground.
Downes could not afford to lose wages by playing cricket. He had married Mary Catherine Reid at Dunedin on 3 June 1891, and they were to have eight children. The Otago Cricket Association, while refusing to pay his wages, did pay Downes something for his services. He was, nevertheless, frequently unavailable for tours outside Otago.
Downes was occasionally involved in disciplinary action. In October 1898 a local umpire accused him of using insulting language, but his apology was accepted and the matter left to rest. However, when another umpire complained within six weeks of a similar incident Downes received a month's suspension. This caused him to miss the Otago versus Canterbury match but not New Zealand's inaugural tour to Victoria and New South Wales in the 1898–99 season.
In December 1910 Downes announced his retirement from first-class cricket, but he was back captaining the Otago team the following season. He was to captain Otago on four occasions and was appointed one of three Otago selectors for the 1912–13 season. His final appearance for Otago was against Canterbury in February 1914. In 51 first-class matches he had taken 311 wickets at a cost of 14.67 runs each, including 20 wickets for 28 runs each in his six matches for New Zealand. Downes continued to play senior cricket for the Grange Cricket Club until 1921–22, having assisted his team to nine senior championship wins. He had also been a capable, aggressive batsman, scoring several centuries in club cricket.
Downes remained active in sport after his retirement from cricket. He refereed club and inter-provincial rugby matches, and controlled the second test between New Zealand and Australia at Dunedin in September 1913. In cricket he umpired local club games, and between the 1925–26 and 1934–35 seasons umpired eight Plunket Shield matches at Carisbrook, and a New Zealand versus Australia match late in the 1927–28 season.
In 1887 Downes had joined the Dunedin City Fire Brigade as an auxiliary fireman, and remained a member for most of his adult life. He retired from A. & T. Burt in October 1945. In January 1949 a presentation was made to him at Carisbrook during the tea break of a representative cricket match.
Alex Downes died at Dunedin on 10 February 1950 shortly after his 82nd birthday, and was buried in Dunedin's Northern cemetery. He was survived by four daughters and three sons, and by his wife, who died on 7 June 1955 at the age of 86.