The Liberal majority in the legislature is now secured by only a few MLAs, and without MLA Kash Heed taking his seat due to family matters, the Liberal margin was down to just four votes.
The budget passed with 45 MLAs in favour and 38 opposed.
The budget will still have to pass a third reading before becoming official.
Losing the second reading vote would likely have meant an early election.
On Monday, Deputy Premier Rich Coleman insisted he wasn't worried.
“Everybody's behind the premier,” he said. “We support the premier, and you'll see it tomorrow when we vote in the house on the budget … our guard is united, and we're going to win the next election."
Clark announced Monday that Multiculturalism Minister John Yap was leaving his cabinet post while her deputy minister, John Dyble, undertook an investigation into the leaked government strategy to woo ethnic voters.
The news came after the premier's then-deputy chief of staff Kim Haakstad, who helped draft the 17-page Multicultural Strategic Outreach Plan more than a year ago, announced she was stepping down on Friday.
Clark has apologized three times for the document, which was leaked by the NDP in the legislature, and the language used in it. The plan made several proposals to entice ethnic voters in the run-up to the May provincial election. It also suggested government resources could be used.
'I will take further action'
Though Clark had said Monday she may yet get caught up in the unfolding scandal, she denied the possibility of that happening after the vote on Tuesday.
Clark had said there may be more action based on the outcome of the report, but she wouldn't detail what action might need to be taken.
While forcing out the premier and B.C. Liberal Party leader just 10 weeks before an election might sound unlikely, Clark told reporters Monday that all options were on the table.
"When we have all the facts and when the report is tabled, we will likely be required to take further action, and I will take further action,” she said in response to questions about whose job might be on the line once an internal investigation is complete.
“When the report comes out and we see what it recommends and what it tells us, I will take action, and you'll see what that means."
Clark’s comments could be a political manoeuvre, but CBC legislative reporter Stephen Smart said the very fact that she allowed the idea to circulate is significant.
But on Tuesday, she dismissed the possibility that she might resign following the result of Dyble's investigation. When asked whether the "further action" she referred to could include stepping down, she told reporters: "No, it won't."
Heed acknowledged there is division in the caucus over Clark's leadership, spurred on by the leaked document.
"She's the leader of the Liberal party and I am a member of that party right now, and I think we'll leave it to the people of B.C. to see whether or not she remains the premier of British Columbia and has the right to govern," he said.
Martyn Brown, Gordon Campbell's former chief of staff, says there's one sure-fire way to unite the party — find a new leader.
"I don't think that Premier Clark can credibly go into an election campaign leading this B.C. Liberal Party having presided over such a scandal," he told CBC News.
Liberal caucus members leaving an emergency meeting with Clark Monday at the legislature said they were united behind her, but were also awaiting the outcome of deputy minister John Dyble's review of the controversial document.
Clark's cabinet ministers said Sunday they supported the premier even though mistakes had been made. Cultural Development Minister Bill Bennett calling the leaked document a "doozy" of a political gaff.
B.C.'s next provincial election is slated for May 14.
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