Fighting as an independent, Dhinakaran bagged 10,421 votes at the end of the second round. He registered 5082 votes in the second and 5,339 in the first.
Ruling AIADMK's E Madhusudanan bagged 4,521 votes at the end of round two. He got 2,738 votes in the first and 1783 in the second.
Led by Chief Minister K Palaniswami and his deputy O Panneerselvam, several ministers had campaigned relentlessly for the party nominee Madhusudanan.
The main opposition party's candidate N Maruthu Ganesh got 1,181 and 1,142 votes respectively in first and second rounds. Counting for third round is on out of a total of 19 scheduled rounds.
With early trends indicating a comfortable win for him, Dhinakaran told reporters in Madurai that it reflected people wanting a change of regime.
"We are the true AIADMK," he said and claimed that the Palaniswami government will "end in three months".
The rival leader has claimed that people have "decided" that he would succeed Amma in the constituency represented twice by her.
Jayalalithaa had won from RK Nagar in the 2015 bypoll and the 2016 assembly general election.
Meanwhile, police and Central armed police forces personnel on security duty brought in more restrictions in and around the counting centre at Queen Mary's College following a disruption.
Counting of votes suffered a temporary disruption following an alleged altercation between supporters of Dhinakaran and AIADMK's E Madhusudhanan.
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