The approval came after the pro-establishment camp voted down a move by opposition lawmakers to adjourn debate over the package. Pan-democrats said the relief failed to help some people, including the elderly, South China Morning Post reported.
Council Front legislator Eddie Chu Hoi-dick, who earlier moved the adjournment motion, also said Beijing's latest criticism on the pro-democracy camp made it impossible for the discussion to continue.
The relief package needed a majority vote in the committee to pass. There are 23 pan-democrats in committee, against 42 pro-establishment or pro-Beijing legislators.
The legislators spent more than 12 hours on Friday debating the administration's HK$137.5 billion injection.
The measures include HK$80 billion worth of wage subsidies to cover up to 50 per cent of workers' salaries for six months, capped at HK$9,000 a month, along with one-off handouts for the hardest-hit sectors.
Pro-establishment lawmakers criticised their political rivals as having turned from an opposition bloc into a "collateral damage camp".
"We are not completely satisfied with the package either. But we should endorse it first to help those who are struggling, and we can work together to press the government for more," said Ann Chiang Lai-wan, of the Democratic Alliance for the Betterment and Progress of Hong Kong.
The deadly contagion has infected at least 1,021 people in the semi-autonomous region and killed four others so far.
( With inputs from ANI )