Legislation creating a new tuition tax credit passed an important first test yesterday in the House Ways and Means Committee, where such bills have always died before.

By a 24-to-13 vote, the committee defeated a motion to table a tuition credit bill on which it now hopes to finish work today. The Senate Finance Committee has approved similar legislation, but the White House and the House leadership both oppose such a step.

The committee later yesterday expanded the bill before it to allow write-offs not only for tuition to private schools, but also for payments to neighboring public school systems - as in cases where District of Columbia parents send youngsters to Maryland public schools.

Yesterday's vote against tabling marked a breakthrough for backers of the tuition credit bill - primarily Catholic school groups, which would benefit from the proposal after being denied direct federal grants before.

Until yesterday, Ways and Means had been a major stumbling block for the tuition credit bill. Largely at Chairman Al Ullman's (D-Ore.) urging, the panel had refused even to consider the measure. The bill passed the Senate repeatedly.

President Carter opposes the tax credit as wasteful, and has introduced a rival bill designed to expand existing federal college scholarships to include more middle and upper-middle-income families.

The two bills now are in a neck-and-neck race in each chamber to see which makes it to the floor first. The House last month refused to take up the Carter bill without a chance to vote on the tuition credit as well.

The bill in Ways and Means would allow parents to reduce their taxes by 25 per cent of their youngsters' tuition to a maximum of $100 for each elementary and highschool pupil and $250 for college students.

The proposal was drafted by Rep. Charles A. Vanik (D-Ohio) to allow a 50 per cent credit, but was cut back in committee on an amendment by Rep. Barber B. Conable (R-N.Y.). The Conable provision was approved 20 to 14.