Unusually, for a high-class hurdler, Kribensis was owned by Sheikh Mohammed and trained by Sir Michael Stoute, both of whom were better known, even in those days, for their exploits in the sphere of Flat racing. On his first appearance at the Cheltenham Festival in 1988, the son of 1980 Derby winner Henbit won the Triumph Hurdle under Richard Dunwoody to provide his distinguished owner with his first ever winner at the March showpiece meeting.
At the start of the 1988/89 season, Kribensis won his first three races, including the Christmas Hurdle at Kempton, all at odds-on, and was consequently sent off 11/8 favourite for his first attempt in the Champion Hurdle at the Cheltenham Festival. The five-year-old gelding was always prominent and led approaching the final flight, but was soon headed, and eased when beaten on the run-in, eventually finished seventh, beaten 11½ lengths, behind shock 50/1 winner Beech Road.
The following season, 1989/90, Kribensis was at the peak of his powers, winning the Fighting Fifth Hurdle at Newcastle, Christmas Hurdle at Kempton and Kingwell Hurdle at Kingwell en route to a second crack at the two-mile hurdling championship. At Cheltenham, he was sent off 95/40 second favourite behind reigning champion Beech Road, at 2/1, but led at the final flight and was driven out to beat Nomadic Way by 3 lengths, thereby recording the first victory in the race for Sheikh Mohammed, Stoute and Dunwoody. Indeed, in so doing, he became the only horse to win the Fighting Fifth Hurdle, Christmas Hurdle and Champion Hurdle in the same season and remains just one of three horses to have won the Triumph Hurdle and Champion Hurdle.