Counting was still ongoing three days after the first parliamentary poll since the defeat of the Islamic State group, but the fiery Shiite preacher's grouping was in the lead with 16 of 18 provinces tallied.
Victory for the veteran nationalist's Marching Towards Reform alliance with Iraq's communists - pitched an anti-corruption outsider force - would be a slap in the face for Iraq's widely reviled ruling establishment.
Sadr - who has ruled himself out of becoming prime minister - looks likely to be the key powerbroker and has already mooted a technocrat government of some dozen parties that bridge sectarian divides.
But with his group set to be far from a majority in parliament, wrangling over any potential coalition should take months - and there remain major obstacles ahead that could thwart Sadr's ambitions.
The elections Saturday - hit by record abstentions - saw a clear rejection of the Iraqi elite that has run the country since the ouster of Saddam Hussein in 2003.
Tallies put the anti-establishment Conquest Alliance of pro-Iranian former paramilitary fighters who helped battle IS in second, and incumbent Prime Minister Haider al-Abadi's bloc back in third.
Abadi - a consensus figure favored by the US - had been seen as likely frontrunner after declaring victory over the jihadists five months ago.
Sadr rose to prominence in the wake of the US invasion, when his militia fighters fought a bloody insurgency against American troops.
After years on the sidelines, he has now reinvented himself as a crusading champion of the poor who has linked up with secularists to battle corruption.