Their first meeting, in Bratislava in 1995, proved to be a turning point, Britain's salutary 5-0 whitewashing by Slovakia forcing them to rise from the Third Division of the Davis Cup, the nation's lowest point.
Kroslak's win last night, 2-6, 7-6, 6-4, did not offer Henman the excuse of struggling on a slow clay court. The British No 1 was unable to make the most of a fast indoor carpet, even though he held a match point at 7-6 in the second set tie-break. The Slovakian world No 79 saved it with a superb service return to Henman's feet, and went on to win the shoot- out, 10-8, with a forehand volley.
It could be said that Kroslak worked his way up to last night's upset, having defeated two other Britons, Martin Lee and Chris Wilkinson, in the qualifying tournament.
But the opening set ran so smoothly for Henman - at least up to the last game, when he had to save a break point for the first time - that Kroslak's revival took everyone but the Slovak by surprise. Breaks in the first and fifth games enabled Henman to take the lead in only 32 minutes.
Kroslak evidently spent much of that time calculating ways to counter Henman's attacking style, and his confidence grew with every winning shot - particularly when taking a swing at the Briton's second serve or his inconsistent forehand.
Henman struggled his way to the tie-break in the second set, forcing his way back from 0-40 in the second game and saving a fourth break point at 3-4. He encouraged his supporters by taking a 3-0 lead in the tie-break, and hit two magnificent forehands to reach the point of victory. But it was not to be.
Kroslak dominated the final set, breaking twice to lead 4-1. Although Henman recovered one break, for 2-4, Kroslak's game was far too solid to crack further, and he produced the winning backhand lob after two hours.
"I think I did pretty much everything out there except win the match," Henman said. "I'm not going to dwell on it... I'm sure I'll bounce back."
Henman's defeat was not the only disappointment. Having billed Boris Becker above Henman and the other home hero, Greg Rusedski, the organisers will "think twice" before agreeing to give the semi-retired former Wimbledon champion a wild card next year.
Becker withdrew from his first-round singles yesterday because of a stomach virus after losing in the doubles on Monday night. It was to have been the German's first singles match in Britain since Pete Sampras defeated him at Wimbledon in 1997.
His countryman, Rainer Schuttler, was at Heathrow airport when the promoters managed to recall him as a lucky loser from the qualifying to replace Becker last night against Karol Kucera, the No 5 seed. Otherwise they would not have had a singles to follow Henman's match.
Becker was not the only player with stomach problems yesterday. A pasty faced Jan-Michael Gambill, who had been ill since arriving from Memphis at the weekend, was dispatched in his opening match by Italy's Davide Sanguinetti, 6-4, 6-4.
Gambill beat Sanguinetti in straight sets when drafted into the United States Davis Cup team for last year's semi-final in Milwaukee, and is expected to be in the team to play Britain in Birmingham at Easter.
"All I know is that Todd Martin is on the team for sure," Gambill, the American No 5, said. "I have spoken to Tom [Gullikson, the captain] and it is a possibility I'll be on the team."
Gambill, ranked No 44, has won both of his matches against Henman, the British No 1. "They've both been really close," Gambill said. "We both serve big, and on those occasions I was just able to make returns a bit better than he did."
Goran Ivanisevic, who was the Wimbledon runner-up for the third time last July, failed to advance beyond the second round for the second year at Battersea. The No 7 seed was defeated by the gifted Moroccan Hicham Arazi, 3-6, 6-3, 6-4. So much for Ivanisevic's 24 aces.
Martina Hingis, the world No 1, wasted no time reaching the quarter-finals of the Paris Indoor Open yesterday, racing to a 6-1, 6-1 victory over the Yugoslav Sandra Nacuk in just 41 minutes.