The 89-33 vote sent the measure to the Senate.
Some legislators complain that the state doesn't prepare for bad economic times when revenues fall short of expectations.
Lawmakers and Gov. Kathleen Sebelius face a projected $682 million budget deficit for the fiscal year that begins July 1, and they appear likely to rely heavily on federal stimulus funds.
The governor and lawmakers are supposed to see that each annual budget leaves cash reserves equal to 7.5 percent of spending. But
the rule is often violated in bad times.
Under the bill, if revenues exceed expectations and the state already has enough cash reserves, the money would go into the special fund.