Contesting alone, the BJP's main rival JMM has won 14 seats and is ahead in four more. The party had contested 79 seats.
Together the BJP-AJSU alliance is headed for the magic figure of 42 in the 81-member house.
If the BJP manages to reach the tally, it will be the first time that Jharkhand will see a majority government after witnessing governments falling like nine pins.
Though the BJP is marching ahead, its heavyweight leader and three-time Chief Minister Arjun Munda lost from Kharsawan.
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However, the party's national vice-president Raghuvar Das won the Jamshedpur East seat.
BJP's alliance partner AJSU suffered a jolt as its chief and former deputy chief minister Sudesh Mahto lost from his home turf Silli, which he had represented for 15 years.
Jharkhand Vikas Morcha (Prajatantrik) has won five seats and is leading in two others, but its chief and Jharkhand's first Chief Minister Babulal Marandi lost from Giridih.
Former CM and Jai Bharat Samanta Party chief Madhu Koda, who was recently chargeesheeted by the CBI in the coal block allocation scam, lost the Majhgaon seat, but his wife Geeta Koda retained the Jaganthpur seat.
The Congress has won three seats and is leading in four others. Its alliance partners RJD and JD(U) are yet to open account.
The BJP has contested 72 seats while its alliance partner AJSU contested 8 seats. Another alliance partner LJP contested one seat. In the 2009 Assembly election the BJP had won 18 seats.