Aam Aadmi Party's prominent faces Atishi and Raghav Chadha, who registered victory in their Assembly election debut, said the mandate has shown that "kaam ki rajneeti" (politics of work) has won and that "work is true nationalism".
Both Ms Atishi and Mr Chadha had unsuccessfully tested waters in the Lok Sabha elections last year.
"It was clear that people of Delhi had made up their minds about Arvind Kejriwal. They voted for him on the basis of his work. It''s ''kaam ki rajneeti'' which has won over the politics of hatred," Ms Atishi told reporters.
Ms Atishi, who was trailing in the early trends, surged towards victory and defeated BJP's Dharambir Singh by a margin of over 11,000 votes.
"Thank you to all the people of Delhi for putting their faith in @AamAadmiParty
and voting for politics of development. In the last 5 years we have endeavoured to make Delhi''s Government Schools the best in the country and now we'll make Kalkaji the best constituency in Delhi!," Ms Atishi tweeted.
Mr Chadha, who replaced sitting MLA Vijender Garg in Rajinder Nagar, defeated BJP's Sardar RP Singh by a margin of over 20,000 votes.
"Mangalwar ko Bajrang Bali ne maza chakha diya (Lord Hanuman taught a lesson to BJP on Tuesday)," he told reporters.
"Delhi's citizens have proved today that what Arvind Kejriwal did in the last five years was true nationalism. Delhi's voters have proved that Kejriwal is a true patriot. They have given their mandate to Kejriwal's model of governance. We will serve the people of Delhi more than we did in the last five years," he added.