The vote sparked protests in Israel and calls for calm from the US and other nations.
It gave initial approval to a plan that would give Mr Netanyahu’s coalition more power over who becomes a judge.
It is part of a broader package of changes that seeks to weaken the country’s Supreme Court and transfer more power to the ruling coalition.
"A great night and a great day," Mr Netanyahu tweeted after the preliminary vote.
He won 64 of the Knesset's 120 seats, making it likely his two revisions on the agenda, the other limiting the Supreme Court's ability to strike down legislation, will be ratified.
Polls have shown most Israelis want the reforms slowed to allow dialogue, or put off completely, Reuters reported.
The vote on part of the legislation is the first of three readings required for parliamentary approval, a process that is expected to take months.
The opposition, including tens of thousands of protesters in front of the Knesset in Jerusalem and in Tel Aviv, saw Monday’s vote as the coalition’s determination to barrel ahead.
Protesters waved Israeli flags and held signs with slogans such as “saving democracy”.
Earlier, a sit-down demonstration was held at the entrance of the homes of some coalition politicians. Traffic was briefly at a standstill on the main road through Tel Aviv.
After the shekel fell by 1 per cent against the dollar, many economists and leaders of high-tech and banking warned of investor and capital flight from Israel.
But Knesset Finance Committee chairman Moshe Gafni, the head of the ultra-Orthodox United Torah Judaism party, said: "There is no link between the justice system reforms and any blow to Israel's economy. Any attempt at linkage is politicised."
Opposition politicians took issue with Mr Gafni's statement, calling the committee "a circus".
Opposition leader Yair Lapid accused the coalition of pushing Israel towards civil war, saying if "you care about Israel and its people" then "you'll halt legislation today".
“We are fighting for our children’s future, for our country’s future. We don’t intend to give up,” he said.
Justice Minister Yariv Levin said: "From now on, the court will belong to everyone."
After the bill passed its first reading, he called on members of the opposition to "come and talk".
"We can reach understandings," Mr Levin said.
President Isaac Herzog has been trying to bring the sides together for talks on the reform with no success.