Forty-six MPs, including cabinet ministers, voted for the key amendments that will come into effect only after another round of voting and government approval. The second and final vote will take place in two weeks.
Four Shiite MPs voted against the law, a pro-Shiite Sunni lawmaker refrained, while two MPs refused to vote.
Shiite MPs have demanded that the new amendments also put into effect the death penalty for anyone who curses their sect's 12 respected Imams, but the Sunni- dominated parliament discarded their requests.
The move to harden penalties for religious crimes came after authorities last month arrested a Shiite tweeter for allegedly cursing the Prophet Mohammed (PBUH), his wife and some companions.
The suspect, Hamad al-Naqi, is being in custody pending further interrogation and trial.
Sectarian tensions have burned in