Johnson began the 1986 World Snooker Championship as a 150–1 outsider, with first-round losses in both of his previous Crucible appearances.

The following year, in the World Championship, Johnson defeated Stephen Hendry 13–12 in the quarter-finals and Neal Foulds 16–9 in the semi-finals.

Johnson won only one match in the final stages of the World Championship thereafter, defeating Cliff Wilson in the first round of the 1988 event.

Johnson dropped out of the top 16 after the 1989–90 snooker season and made his last Crucible appearance in 1991, losing in the first round to Dennis Taylor.

[3][9] Johnson achieved little success in his early professional career and gained a reputation for not performing well in televised matches.

[10] Johnson won the billiards competition that was running alongside the snooker event, defeating Ian Williamson 500–284 in the final.

He next eliminated Jim Wych 5–2, which was the most significant win of Johnson's professional career up to that point, but he then lost in the last-24 round to Graham Miles, 3–5.

[17][15] Johnson defeated Vic Harris 9–4 in the qualifying rounds of the 1982 World Championship and reached the last 48, where he lost 8–9 to Mike Hallett.

[15] After receiving a walkover against John Phillips, Johnson faced Cliff Wilson in the qualifying competition for the 1982 Jameson International.

[24] At the 1983 UK Championship, Johnson reached the quarter-finals by eliminating Matt Gibson and Virgo (both by 9–6) and David Taylor 9–3.

[25] In the qualifying event for the 1984 World Championship, he won his encounter with Gibson 10–3 to earn his debut on the Crucible stage[22][26] (where he was defeated 1–10 by Dennis Taylor).

[27] At the 1984 Costa Del Sol Classic, he started with a quarter-final win against Mick Fisher and lost 2–3 in the semi-final to Dennis Taylor.

[22] In the following ranking event, the 1984 Grand Prix, Johnson defeated Paul Medati 5–1 but lost 4–5 to Ian Williamson in the last 32.

[29] According to Janice Hale of The Daily Telegraph, Johnson "failed to reproduce any of the fighting form which he displayed in the final of last season's Professional Players Tournament" as he lost 2–9 to Thorburn.

[33][38] He eliminated Tony Knowles despite taking painkillers for a cyst on his back before the start of play, winning the last two frames of the final session for a 16–8 victory.

[34][39][40] In the final, Johnson met world number one Steve Davis; they had never previously played a professional match against one another.

[43] Gordon Burn wrote in his book Pocket Money (1986), "From the beginning of the third session he played an open game full of flair and daring and the length-of-the-table, long-potting which had been so characteristic of Steve Davis in the days when he was still making his name.

[52] Johnson was runner-up to Dennis Taylor in the four-player 1987 Carling Challenge,[53] and he won the 1987 Scottish Masters by overcoming Terry Griffiths 9–7 in the final for his only other major professional snooker title.

[54][55] He reached the semi-finals of the 1987 UK Championship, where he came close to making a 147 maximum break against Jimmy White but missed the pink on 134[32] and lost the match 4–9.

[22] Later that season Johnson reached the semi-finals of the 1988 Masters, where he lost 3–6 to Davis after eliminating Willie Thorne and White.

[57] Dropping six places to 11th in the 1988–89 season,[58] Johnson's best showing in a ranking tournament was reaching the quarter-finals of the 1988 Fidelity International Open.

[22] Johnson won the invitational 1989 Norwich Union Grand Prix by defeating Hendry 5–3 in the final,[59] but lost 8–10 to Darren Morgan in the opening round of the 1990 World Championship.

[61] Johnson won the 1991 Nescafe Extra Challenge, a four-player round-robin event, with victories in all three of his matches, against Tony Drago, James Wattana and Alain Robidoux.

[22] Johnson was runner-up to Stephen Hendry in the invitational 1992 European Challenge,[65] and he narrowly missed qualifying for the 1992 World Championship after losing 9–10 to Mick Price on the pink ball in the deciding frame.

[67] He broke his ankle in a fall at home before the start of the 2003–04 season and did not compete in any events until the World Championship qualifying in February 2004.

[68][69] He played his last match as a professional later that month in the qualifying rounds of the 2004 Players Championship, where he lost 3–5 to Stuart Mann.

[71] Johnson played in the 2000 World Seniors Masters, a one-frame-format event, and lost in the first round to the eventual champion Willie Thorne.

[74] Johnson won the April 2019 World Seniors Masters, with all three of his matches determined on a re-spotted black used as a tiebreaker in the event of each player winning one of two frames.

[79] Snooker journalist Hector Nunns wrote in 2017 that Johnson would always be remembered for "his shot-making, his shoes, his extra-curricular singing, and his sheer joie de vivre in the match that defined his career".

[81][82] In April 1987, BBC1 broadcast a 30-minute profile of Johnson, An Ordinary Joe, which focused on the year since his World Championship victory.