Kaur, wife of former chief minister Amarinder Singh, won by a margin of over 23,282 votes, an election office spokesman said.
The seat fell vacant after Amarinder got elected to Lok Sabha from Amritsar.
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Patiala seat was retained by Congress.
Kaur polled 52,967 votes, SAD nominee Bhagwan Dass Juneja 29,685 and Aam Aadmi Party (AAP) candidate Harjit S Adaltiwala 5724 votes.