Mayor de Blasio’s controversial plan to ditch the admission test for the city’s top high schools won a razor-thin approval from the Assembly’s Education Committee on Wednesday morning — but one backer vowed to withdraw her support unless changes were made.

A bill to advance the mayor’s proposal passed the 30-member committee by just 16 votes, with all eight Republicans and four Democrats voting against it. Two legislators were absent.

Committee Chairwoman Catherine Nolan (D-Long Island City) and Assemblywoman Amy Paulin (D-Scarsdale) both said they voted in favor to spur further discussion of the issue, with Paulin — who said the plan “does feel like a quota to me” — pledging to oppose the bill if it goes to the Assembly floor as currently written.

Paulin also blasted de Blasio for pushing the measure — introduced late Friday by Assemblyman Charles Barron (D-Brooklyn) — so close to the scheduled June 20 end of the legislative session.

“We should have had hearings. We should have had conversations. The mayor was wrong to bring it forward this like this,” she said.

The bill now goes to the Assembly’s Rules Committee for further consideration.

De Blasio needs a change in state law to eliminate the “Specialized High School Admission Test” as part of a plan to diversify the city’s eight elite high schools by instead populating them with the top 7 percent of students at each city middle school.