Lawmakers overwhelmingly ­approved a massive health care cost-control experiment Tuesday that they predicted will save billions of dollars over the next 15 years. But some industry leaders cautioned that it relies heavily on unproven tools to achieve the savings.

The plan, which Governor Deval Patrick said he would sign into law, contains many of the most promising ideas for curbing health care costs. Legislators and the governor are counting on saving $200 billion through a first-in-the-nation statewide medical spending target tied to the overall growth of the state economy, a transition to a budget-minded payment system for hospitals and doctors, the growth of large provider organizations to ­coordinate care, and greater cost transparency for consumers.