The flotation of the business, behind brands such as Sheila's Wheels, will also allow founder and chairman Peter Wood to bank £186m by reducing his stake by one-third.
Penta joined with hedge fund manager Toscafund to arrange and lead the £190m equity investment that helped Mr Wood buy out the 70% stake held by part-nationalised Lloyds Banking Group in February 2010.
That deal valued esure at about £260m.
Esure priced the sale of 50% of the business at 290p a share, towards the upper end of its original 240p to 310p range.
Its shares closed at 307p, a gain of 27p, or 5.9%, on the day.
The sale of new shares will raise £50m for esure which it will use to repay debt.
Penta's fund, Tosca Penta Investments, which had just over 37% of esure before the listing, will retain around 11.6% of the company.
If there is demand it will sell another £90m of shares under an overallotment option, which would reduce its stake to 4.1%.
David Calder, founding partner at Penta and an esure director, said: "This initial public offering is testimony to the strength of the company, its brands and most importantly its management and staff who deserve all their success."
His colleague Charles Schrager added: "The IPO exit, together with earlier returns of capital, will generate a money multiple of over 3.3 times for Tosca Penta Investments."
Esure, which employs 750 people in a contact centre in Glasgow, said 10.8% of its offering had been bought by retail investors.
Mr Wood will remain esure's largest shareholder with a 30.9% stake.
Mr Wood, who previously launched Direct Line for Royal Bank of Scotland, founded esure 13 years ago as a joint venture with mortgage lender Halifax, which became part of HBOS then Lloyds.
The Surrey-based company had 1.75 million motor and home policies in force as of December 31, 2012.