The Environmental Protection Agency, emerging victorious from a tense meeting with the Office of Management and Budget, announced yesterday that makers of heavy-duty trucks, vans and buses must start cleaning up their diesel exhausts by 1988.

The new standards are to be installed in three stages, EPA officials said, with minor improvements slated for 1988 and progressively tougher standards going into effect in 1991 and 1994.

According to EPA officials, the phase-in will give truck and bus manufacturers time to develop technology needed to trap and burn away fine soot particles that have made diesel smoke a growing air pollution problem, especially in urban areas.

"This will drastically reduce particulate emissions," said Richard D. Wilson, head of the EPA's mobile sources division.

As late as yesterday morning, however, there was considerable doubt that the EPA would succeed in issuing the new standards, required by a court order.

According to EPA officials, the OMB believed that the proposed rules were too stringent and was arguing that only the first phase of the three-step control strategy should be announced.

"Basically, they seemed to be saying, 'We don't think you need to make all these long-term decisions to comply with the court order,' " Wilson said. "They were saying we shouldn't do more than was needed to comply with the court order."

EPA Administrator Lee M. Thomas met with OMB Director David A. Stockman yesterday afternoon to argue the agency's case. Apparently, he was able to persuade Stockman that the court order required the agency to set the stricter standards as a way to compel truck makers to develop emission-trapping devices.

Manufacturers of some foreign-made diesel automobiles, including Mercedes and Volkswagen, have developed such devices, and EPA officials have said they believe that the technology could be transferred to heavier-duty vehicles.

The outcome of yesterday's meeting was applauded by environmentalists, who nevertheless complained that the emission standard was late in coming and could have been phased in earlier.

"It's good that Lee Thomas and not David Stockman made the decision, but it has be borne in mind that the rule Thomas brought in was already heavily compromised," said David Doniger, an attorney with the Natural Resources Defense Council.