Mr Dariye has been accused of money laundering by British authorities.
'Joke'
Last week, eight of Plateau state assembly's 24 legislators served an impeachment notice on Mr Dariye, citing corruption charges which they asked the governor to defend, or lose his position.
Mr Dariye dismissed the impeachment notice served on him as "a joke", saying the legislators had failed to form a quorum as required by the Nigerian constitution and so lacked the powers to initiate impeachment proceedings against him in the state assembly.
The eight lawmakers, all in the custody of the Economic and Financial Crimes Commission in the country's capital, Abuja, on Friday returned to Jos under armed guard to commence impeachment proceedings against Mr Dariye.
All of Plateau state's assembly members are being investigated by the EFCC.
The governor's supporters tried to stop them from entering the state assembly premises by mounting road blocks and burning used tyres along the way leading into the assembly.
Riot police fired tear gas to disperse them.
But the protesters regrouped and returned to the assembly premises, where they hurled stones at the lawmakers and their police escorts.
The riot police, who feared that they might be overpowered by the protesters fired into the crowd, killing two people and seriously injuring another, police sources told the BBC.
A Reuters reporter in Jos says he saw "the corpse of one man shot through the eye" and "another man [who] was taken to hospital with bullet wounds in his leg and abdomen."
Eyewitness Musa Abdullahi says the home of the deputy president of the Nigerian senate was also set ablaze during the protests.
Deputy senate president Ibrahim Nasir Mantu is believed to be supportive of the move by the EFCC to prosecute Mr Dariye.