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Sanjrani secured 57 votes, while the rival candidate Raja Zafarul Haq of PML-N secured 46 votes.
Voting took place through secret ballot.
Earlier, Newly-elected members of the upper house took oath as Senators at a specially convened session of the house in Islamabad on Monday morning.
Senator Sardar Yaqoob Khan Nasir, who was nominated by the President to chair the session administered oath to the new members.
Fifty-two of fifty-three newly elected Senators took oath .
They included a member elected from Punjab against the seat vacated due to disqualification of Nehal Hashmi.
Ishaq Dar, who is under treatment abroad, could not attend the session.
After oath-taking the new members signed the roll of the house.