The New York company finished up 23.6% to $69.22 after opening 18% above its initial public offering price.
The stock opened at $66. On Tuesday, UniPath priced its initial public offering of 23.9 million shares at $56 each.
The company said that it planned to raise $1.3 billion in the IPO on the New York Stock Exchange.
The shares had been marketed for an estimated $52 to $54, which the company elevated on Monday from $43 to $50.
UiPath is offering 9.4 million Class A common shares, while certain holders are offering 14.5 million. UiPath gave the underwriters a 30-day option on 3.6 million more shares.
The company said it would use the proceeds for general purposes, including working capital, operating costs and capital spending.
The company was founded in Bucharest in 2005 under the name DeskOver by the entrepreneurs Daniel Dines and Marius Tirca.
It was rebranded 10 years later as UiPath and is based in New York. It has 50 offices in North America, Europe and Asia.
"From 10 people in an apartment in Romania in 2015," Dines, the CEO, wrote in a company filing, "we grew six years into a multinational business in nearly 30 countries, with $580 million in annual recurring revenue, being one of the fastest growing modern enterprise software ever."
In the year ended Jan. 31, UiPath narrowed its net loss to $92.3 million, or 55 cents a share, from $519.9 million, or $3.41 a share, in fiscal 2020.
In March, UiPath acquired the application programming interface integration platform Cloud Elements.
Morgan Stanley and J.P. Morgan are lead bookrunners for the offering. Bank of America Securities, Credit Suisse, Barclays, and Wells Fargo Securities are active bookrunners.