ISLAMABAD—Pakistan’s parliament is emerging as the main beneficiary of the country’s crisis as the monthslong protests in Islamabad weaken along with their main target, Prime Minister Nawaz Sharif.

Opposition politician Imran Khan, who continues to lead protests even after the larger contingent drawn by cleric Tahir ul Qadir pulled out last month, accuses the prime minister of rigging the May 2013 election, a charge Mr Sharif rejects. In the initial days of the protest, which began in Islamabad on Aug. 15, Mr. Sharif’s government...