WASHINGTON — The Senate, in a predawn vote two hours after the deadline passed to avert automatic tax increases, overwhelmingly approved legislation on Tuesday that would allow tax rates to rise only on affluent Americans while temporarily suspending sweeping, across-the-board spending cuts.

The deal, worked out in furious negotiations between Vice President Joseph R. Biden Jr. and the Republican Senate leader, Mitch McConnell, passed 89 to 8, with just three Democrats and five Republicans voting no. Although it lost the support of some of the Senate’s most conservative members, the broad coalition that pushed the accord across the finish line could portend swift House passage as early as New Year’s Day.

Quick passage before the markets reopen on Wednesday would be likely to negate any economic damage from Tuesday’s breach of the “fiscal cliff” and largely spare the nation’s economy from the one-two punch of large tax increases and across-the-board military and domestic spending cuts in the New Year.

“This shouldn’t be the model for how to do things around here,” Mr. McConnell said just after 1:30 a.m. “But I think we can say we’ve done some good for the country.”