Evans was born in Manhattan on March 22, 1932, and learned much about the game by playing for ten cents an hour on 42nd Street in New York City,quickly becoming a rising star. At age 14, he tied for fourth-fifth place in the Marshall Chess Club championship. The next year he won it outright, becoming the youngest Marshall champion up until that time. He also finished equal second in the U.S. Junior Championship, which led to an article in the September 1947 issue of Chess Review. At 16, he played in the 1948 U.S. Chess Championship, his first, tying for eighth place at 11.5-7.5. Evans tied with Arthur Bisguier for first place in the U.S. Junior Chess Championship of 1949. By age 18, he had won a New York State championship as well as a gold medal in the Dubrovnik Chess Olympiad of 1950. In the latter, his 90% score (eight wins and two draws) on sixth board tied with Rabar of Yugoslavia for the best result of the entire Olympiad. In 1951, he first won the U.S. Championship, ahead of Samuel Reshevsky, who had tied for third-fourth in the 1948 World Championship match-tournament. Evans won his second championship the following year by winning a title match against Herman Steiner. He won the national championship thrice more - in 1961-62, 1967-68 and 1980, the last in a tie with Walter Browne and Larry Christiansen.

FIDE awarded Evans the titles of International Master (1952) and International Grandmaster (1957). In 1956 the U.S. State Department appointed him a "chess ambassador".

Evans performed well in many U.S. events during the 1960s and 1970s but his trips abroad to international tournaments were infrequent and less successful. He won the U.S. Open Chess Championship in 1951, 1952, 1954 (he tied with Arturo Pomar but won the title on the tie-break) and tied with Walter Browne in 1971. He also won the first Lone Pine tournament in 1971. He represented the U.S. in eight Chess Olympiads over a period of twenty-six years, winning gold (1950), silver (1958), and bronze (1976) medals for his play, and participating in team gold (1976) and silver (1966) medals.

His best results on foreign soil included two wins at the Canadian Open Chess Championship, 1956 in Montreal, and 1966 in Kingston, Ontario. He tied for first-second in the 1975 Portimão, Portugal International and for second-third with World Champion Tigran Petrosian, behind Jan Hein Donner, in Venice, 1967. However, his first, and what ultimately proved to be his only, chance in the World Chess Championship cycle ended with a disappointing 14th place (10/23) in the 1964 Amsterdam Interzonal.

He never entered the world championship cycle again, and concentrated his efforts on assisting his fellow American Bobby Fischer in his quest for the world title. He was Fischer's second for the Candidates matches leading up to the World Chess Championship 1972 against Boris Spassky, though not for the championship match itself, after a disagreement with Fischer.

At his peak in October 1968 he was rated 2631 by the United States Chess Federation.

Evans had always been interested in writing as well as playing. By the age of eighteen, he had already published David Bronstein's Best Games of Chess, 1944-1949 and the Vienna International Tournament, 1922. His book New Ideas in Chess was published in 1958, and was later reprinted. Over the years he has written or co-written more than 20 books on chess.

He wrote the tenth edition of the important openings treatise Modern Chess Openings (1965), co-authored with editor Walter Korn. He also made a significant contribution to Fischer's My 60 Memorable Games (1969), writing the introductions to each of the games and urging the future World Champion to publish when he had initially been reluctant to do so. Some of Evans's other books are Modern Chess Brilliancies (1970), What's The Best Move (1973), and Test Your Chess I.Q. (2001).

Evans began his career in chess journalism during the 1960s, helping to found the American Chess Quarterly, which ran from 1961-65. He was an editor of Chess Digest during the 1960s and 1970s. For over thirty years, until 2006, he wrote a question-and-answer column for Chess Life, the official publication of the United States Chess Federation (USCF), and has also written for Chess Life Online. His weekly chess column, Evans on Chess, has appeared in more than fifty separate newspapers throughout the United States. He also writes a column for the World Chess Network.

Evans has also commentated on some of the most important matches for Time magazine and ABC's Wide World of Sports, including the 1972 Fischer versus Spassky match, the 1993 PCA world title battle between Garry Kasparov and Nigel Short and the Braingames world chess championship match between Vladimir Kramnik and Garry Kasparov in 2000.

Evans also contributed a large amount of tutorial and other content to the Chessmaster computer game series, most notably an endgame quiz and annotations of classic chess games. His contributions to chess writing and journalism have earned him many awards, including the USCF's Chess Journalist of the Year award in 2000. He was inducted into the U.S. Chess Hall of Fame in 1994.

Chess historian Edward Winter has criticized Evans's work, asserting that it is sloppy, dishonest, and riddled with factual inaccuracies, though these claims have been denounced by Larry Parr.

This game, against future grandmaster Abe Yanofsky, who had won the brilliancy prize against Botvinnik at Groningen the year before, was Evans's first victory against a noted player:

Yanofsky - Evans, U.S. Open 1947, Alekhine defence B05

1. e4 Nf6 2. e5 Nd5 3. d4 d6 4. Nf3 Bg4 5. h3 Bxf3 6. Qxf3 dxe5 7. dxd5 e6 8. a3 Nc6 9. Bb5 Qd7 10. c4 Nde7 11. 0-0 Qd4 12. Bg5 a6 13. Bxe7 axb5 14. Bxf8 Rxf8 15. cxb5 Nxe5 16. Qe2 0-0-0 17. Nc3 Ng6 18. Rad1 Qe5 19. Qc2 Rxd1 20. Rxd1 Rd8 21. Rc1 Nf4 22. Kh1 Qh5 24. Kh2 Rd3 25. f3     (see diagram at left)

25 ...Rxf3!   26. Rd1 Nxh3! 27. gxf3 Nf2+ 28. Kg3 Qh3+ 29. Kf4 Qh2+ 30. Ke3 (0–1)

See the game online