Up to the final minutes, it was not clear the bill would pass and many Democrats held their votes, allowing the tally to creep slowly and giving no indication which way it might fall.
The bill now moves to the House.
"According to Politico, Pelosi said she will not be voting for the bill: "'I'm pleased with the product, I'm not pleased with the process, ' Pelosi told reporters Thursday, later adding she plans to vote against the bill but confirmed she isn't formally whipping against it.
Top Senate Democrat Chuck Schumer warned that the delay put lawmakers "in risky territory", and a number of fellow Republicans including Senator John Cornyn confronted Paul in the chamber about his strategy.
Paul's protest forced Congress to miss a midnight deadline for passing a funding measure to keep the government operating.
But the libertarian, failed 2016 GOP presidential contender and "wacko bird" - a moniker an angry Sen.
Rep. Cheri Bustos, a Democrat who represents a swing district in IL, told USA TODAY on Thursday she thought the bill was a good deal for Democrats. The deal found support in both parties largely because it has something for everyone - both the military spending Republicans wanted and the money for domestic programs Democrats sought.
The Senate also approved the measure earlier on Friday morning.
But the bill's path through the House could prove dicey.
Added conservative Democrat Henry Cuellar of Texas, "It's an easy 'yes'".
The Office of Management and Budget has officially ordered the USA government closed.
As the House voted on the procedural measure in the middle of the night, the mood in the House chamber was rather relaxed, reports CBS News' Rebecca Kaplan.
The USD 300 billion in spending included in the bill just approved will ensure the annual budget deficit will exceed USD 1 trillion in 2019, said the Committee for a Responsible Federal Budget, a private fiscal policy watchdog group in Washington.
Pence is in South Korea, where he is leading the US delegation to the opening ceremonies of the Winter Olympics.
Body of missing Filipino found in Taiwan quake
Taiwan's National Fire Agency said Thursday that 10 people were killed, 272 injured and seven remained unaccounted for. Firefighters climbed ladders hoisted against windows to reach people inside apartments.
That vote was delayed until 2 a.m.by Sen.
In the House, Democratic leader Nancy Pelosi is opposing the deal and pressuring House Speaker Paul Ryan, to promise an open debate on legislation to protect the DREAMers - something McConnell has promised Senate Democrats. The House had already voted on a short-term funding measure, known as a continuing resolution (CR), earlier this week that also expired March 23, but provided a boost in funding to the Pentagon through September.
As the clock hit midnight, Office of Management and Budget Director Mick Mulvaney immediately issued an order to close non-essential government operations.
The Senate is expected to vote on a budget deal at 1 a.m. and then the House will vote. Military and essential workers would remain on the job regardless.
A shutdown - technically a lapse in agency appropriations - became inevitable as GOP Sen.
Paul voted for the deficit-financed tax bill in December.
Republicans were sheepish about the bushels of dollars for Democratic priorities and the return next year of $1 trillion-plus deficits.
The Senate is likely to vote to reopen the government in the wee hours Friday. It's the second time this year lawmakers have let funding lapse while they staged standoffs meant to draw attention to their causes.
Pence is set to lead the US delegation to the opening ceremonies of the Winter Games in Pyeongchang, South Korea, Friday evening.
At the White House, there appeared to be little sense of concern. That suggested a short shutdown, if any, less than a month after the three-day interruption last month. But the government stumbled into the shutdown, the second in three weeks, at midnight after a single senator mounted a protest over the budget-busting deal and refused to give in.
Mr Paul was unfazed, saying: "I didn't come up here to be part of somebody's club".
He says senators will likely pass the bill, adding, "They'll be exhausted and ornery, but it's their own fault".
Rep. Steny Hoyer of Maryland says Democrats would support such a move.
Paul explained in an interview with Fox News Thursday afternoon why he blocked the vote on the measure: he objects to the inclusion of the bipartisan budget deal to lift spending caps. The aide requested anonymity because leadership deliberations are secret.