The British No 1 triumphed 7-6, 6-4 in 83 minutes to qualify for next week's tournament in Hannover, despite feeling under the weather and receiving treatment on court for a headache in the opening set.
The left-hander joins Pete Sampras, Michael Chang, Patrick Rafter and Jonas Bjorkman at the eight-man finale. Three more places are still to be decided.
Rusedski needed the visit from his coach after taking a 5-4 lead in the first set. Four games earlier, the world No 5 had recovered from two double faults by firing over three aces.
When the set went to a tie-break, the Briton's serve proved a useful weapon. Rusedski won the decider 7-3 as Kulti double-faulted in front of several thousand home fans.
The Briton claimed his historic victory on a second match-point with a winning volley.
Earlier, Britain's No 2, Tim Henman, took just over two hours to beat American qualifier David Wheaton, who is ranked 150th in the world.
Henman, whose early defeat in Paris last week denied him a place in Hannover, had plenty of chances to secure an early win in the match, but could convert only four out of 14 break-points.
A listless first set was quickly forgotten as Henman finally managed to find his game and win 1-6, 6-1, 7-6.
"I felt like I was just going through the motions in the first set," the 23-year-old from Oxford said. "He played well in the first set, but I suddenly felt that I wanted to salvage something from this match."
Thomas Muster kept alive his hopes of making the Hannover event by beating Norway's Christian Ruud 6-3, 6-1. The Austrian is currently occupying the final place in the rankings. France's Cedric Pioline beat American Richey Reneberg 6-4, 6-4.Reuse content