A hard-tackling right full back, Stevens advanced through Everton's youth ranks as manager Howard Kendall steadily built a new young side to rival their great foes Liverpool, who were winning trophies and dominating the English game while Everton had been without a domestic honour since 1970.
Stevens made his Everton debut in 1982 and settled into the senior game quickly as Kendall's otherwise ageing side struggled to make an impact on their rivals and on the top flight in general. However, with a few astute signings and one or two more graduates from the ranks, Everton reached the FA Cup final in 1984, having already lost to their great rivals in the League Cup final earlier in the season.
Stevens played his part in Everton's opening goal at Wembley against Watford - his pace enabling him to reach a loose ball from a half-cleared cross first and set up Graeme Sharp for a clinical finish. Everton won 2-0.
The following year, Stevens was an integral part of the Everton team which chased a treble of League championship, FA Cup and European Cup Winners Cup. The title was clinched but Everton were beaten by Manchester United (reduced to 10 men after Kevin Moran was sent off) in the FA Cup final. However, a glorious and eventful run in Europe ended in triumph for Everton and Stevens when the Cup Winners Cup was clinched, thanks to a 3-1 win over Rapid Vienna. The only downside of such a successful season was that the Heysel Stadium disaster and subsequent disqualification of all English clubs from European competition meant that Everton were disallowed from trying their luck in the European Cup the following year.
Stevens was again a regular as Everton aimed to defend their League title in 1986, but a rejuvenated Liverpool overhauled them. The two also met in the FA Cup final - the first ever all-Merseyside affair - and Liverpool won that game 3-1 to clinch only the third modern-day "double". Stevens shouldered some of the blame - he played a loose pass which was intercepted by Liverpool's Ronnie Whelan and led to an equaliser for the men in red, who went on to win 3-1.
Stevens was named in the squad for the 1986 World Cup (along with the Tottenham Hotspur player Gary Stevens, causing a spot of confusion and played in all of the games as England reached the quarter finals, where they were beaten controversially by Argentina, who went on to win the tournament.
Back at Everton, Stevens again played frequently as the blue half of Merseyside regained the League championship in 1987, although he did incur the wrath of Liverpool fans when a tackle on left back Jim Beglin left the Liverpool player with a badly broken leg, which finally led to his retirement from playing in 1990.
In the same year, England also qualified for the 1988 European Championships with Stevens in his familiar No.2 shirt. By now one or two critics had started to scorn him for supposedly poor positional play and ball distribution, but his coaches at club and international level kept resolute faith in him.
At club level, 1988 was not successful for Everton, although Stevens did score a famous goal to give Everton a 1-0 win over Liverpool in the League Cup, at a time when Liverpool were in the process of a 29-game unbeaten start to the league season. Everton were trophyless once again, but England had the European Championships in West Germany to look forward to.
Unfortunately, the competition was a disaster for both England and Stevens. After a shock defeat to the Republic of Ireland, England went into the tough second group game against the Netherlands needing to win. Stevens was, however, instrumental in the defeat which followed, losing the ball to Ruud Gullit down the flank, which led to the opening goal of a famous hat-trick by Marco Van Basten. Stevens had come close to blocking Van Basten's shot when he'd been caught napping wide on the flank seconds earlier by Gullit, showing his speed and determination, but it was tough to accept as England wimped out of the tournament without a point.
After the competition, Everton accepted a bid of one and a quarter million pounds from Glasgow Rangers for Stevens to move north of the border. He retained his England place, having seen off long-term rival Viv Anderson (who had held the slot from the late 1970s up to the mid 1980s), though had to contend with the emergence of Paul Parker of Queens Park Rangers as a serious rival for his place.
Rangers were in the midst of a revolution when Stevens joined, with manager Graeme Souness unashamedly buying non-Scottish players (including many Englishmen) to bolster his side. Stevens' first season ended with a Scottish Premier Division title. He would win five more, plus two Scottish Cups and three Scottish League Cups.
When England qualified for the 1990 World Cup in Italy, Stevens was duly named in the squad though again a handful of critics had been scathing of his displays. However, he was in the side which faced the Republic of Ireland in the opening game. It ended 1-1 - not a disaster, but there were clear problems with the England personnel and tactics and Robson made changes for the next game. Stevens was replaced by Parker, who played so well (despite being more usually a central defender for QPR) that he kept his place up to and including England's dramatic semi-final exit on penalties against West Germany, the eventual winners. Stevens was recalled to play the host nation in the meaningless third place play-off, which England lost 2-1.
Parker's emergence - plus that of Arsenal right-back Lee Dixon - left Stevens looking increasingly out of the frame for international football, especially as Robson had quit to return to club football, but he stuck around sporadically for the next two years, getting occasional starts and sub appearances under Graham Taylor.
England qualified for the 1992 European Championships but Stevens was left out of Taylor's initial squad in favour of Dixon. When Dixon got injured in the grace period prior to the deadline for squad confirmation, Stevens was recalled, but then he too suffered an injury and withdrew. England ended up taking part in the competition without a recognised right back, and exited in the group stage. Stevens had played his last game for his country. His international career ended with 46 appearances, although he never scored a goal.
Stevens continued to play for Rangers until 1994, and in 1993 was a key player in their treble winning side. He then returned to Merseyside to see out his career with Tranmere Rovers in a 350,000 pound deal. In his first season, Tranmere reached the playoffs, but a semi-final defeat by Reading ended their hopes of Premier League football.
He retired in 1998 and after a spell as a physiotherapist with the Bolton Wanderers Academy he became a coach at Chester City. Everton fans later named him as the right back in the club's all-time greatest XI in a poll on the club's website. The XI also featured six others from the mid-1980s era.