Jordan entered 1998 with significant expectations: the team had finished fifth in the Constructors' Championship in 1997 and now had a proven race winner in Damon Hill, who joined from Arrows after a difficult 1997 season. Ralf Schumacher, who had impressed in his rookie year with the team, was retained for a second season. Test driver Pedro de la Rosa also drove the 198 during development sessions.
The car was powered by a Mugen Honda V10, Goodyear tyres and was fuelled by Total.
Despite promising pre-season test times, the 198 struggled badly in the opening half of the championship. Hill reported chronic understeer, and the Mugen Honda engine was down on power compared to the Renault and Mercedes units at the front of the field. Jordan failed to score a point in the first half of the season — a performance that led to consequences within the team's technical structure.
Designer Gary Anderson, who had created every Jordan Formula One car since the team's debut in 1991, departed mid-season. Eddie Jordan brought in Mike Gascoyne to lead a comprehensive revision programme. The 198's suspension, front wing and floor were all overhauled, while Mugen's engineers worked to improve engine output. Goodyear's tyre development programme also contributed to a marked improvement in the car's balance.
The transformation was dramatic. Jordan scored points in every race but one during the second half of the season. The culmination came at the Belgian Grand Prix at Spa-Francorchamps, a race run in chaotic wet conditions. Hill led home Schumacher in a historic Jordan one-two, delivering the team their first World Championship victory at the fourteenth attempt. It was also Hill's first win since his 1996 title-winning season and the only victory of his final year in Formula One.
Schumacher added a third-place finish at the Italian Grand Prix in Monza, while Hill claimed fourth on three separate occasions. The team ended the season fourth in the Constructors' Championship with 34 points — four behind Williams in third and one ahead of Benetton in fifth.
Benson and Hedges continued as title sponsor for a third consecutive year, and the 198 wore a "hornet" livery: a hornet's head and eye on either side of the nosecone, wing markings and stripe detailing along the car's flanks. At the French, British and German Grands Prix, where tobacco advertising was restricted, the Benson and Hedges name was replaced with "Buzzin Hornets." The team also carried MasterCard branding on the airbox following the collapse of the Lola-based MasterCard Lola team before the 1997 season had even started.
The Jordan 198 holds a unique place in the team's history as the car that ended Jordan's wait for a Formula One victory. The Spa one-two remains one of the most dramatic results in the team's story, achieved against the odds after a demoralising first half of the season. Mike Gascoyne's mid-season intervention and the Mugen Honda engine development together demonstrated that Jordan could adapt and recover, qualities that would sustain the team through several more competitive seasons before its eventual decline and sale in 2004.