Playing with European Ryder Cup Captain Paul McGinley on the day qualification for next year's side began, Challenge Tour winner Kofstad birdied the 15th, 16th and 17th before producing an eagle three at the last at Celtic Manor.
That saw the Norwegian finish with a seven-under-par 64 over the Twenty ten Course that hosted The Ryder Cup three years ago.
Kofstad finished the day two shots clear of England's Chris Wood and Australian Richard Green, with Tjaart Van Der Walt, Mark Foster and Gregory Bourdy on four under.
McGinley had started the points race with a bogey, but recovered to shoot a one under 70 and high-fived the 26-year-old Kofstad after holing a bunker shot on the last.
"What a finish," McGinley said of Kofstad.
"To finish birdie, birdie, birdie, eagle is fantastic.
"He hit it a million miles, hit a lot of fairways, played very well and he deserved that score."
Kofstad won the Challenge Tour last season but is 149th on The Race to Dubai after missing eight cuts in succession following his only top-ten finish of the year at the Spanish Open in April.
A neck injury also forced him to withdraw from the French Open but working with a sports psychologist has seemingly had the desired effect.
"I have been very, very calm the last two weeks," Kofstad said.
"I started to settle down a bit.
"I had been a bit stressed and tentative and wasn't able to practice as much as I wanted to with my neck injury."
Selected first-round scores from the Wales Open on Thursday (GBR and IRL unless stated, par 71):
64 - Espen Kofstad (NOR)
66 - Chris Wood, Richard Green (AUS)
67 - Tjaart Van Der Walt (RSA), Gregory Bourdy (FRA), Mark Foster
68 - Emiliano Grillo (ARG), Robert Rock
69 - Soren Kjeldsen (DEN), Peter Uihlein (USA), Liam Bond, Mikko Ilonen (FIN), Maximilian Kieffer (GER), Robert Coles
70 - Christian Cevaer (FRA), Damien McGrane, Ricardo Santos (POR), Raphael Jacquelin (FRA), Simon Wakefield, David Drysdale, Callum Macaulay, Alessandro Tadini (ITA), Keith Horne (RSA), Paul McGinley, Gonzalo Fdez-Castano (ESP),Gregory Havret (FRA)
71 - John Parry, Ross Fisher, Anders Hansen (DEN), Jorge Campillo (ESP), Mikko Korhonen (FIN), Tom Lewis, Oliver Fisher, Thongchai Jaidee (THA), Jose-Maria Olazabal (ESP), Eduardo De La Riva (ESP), Michael Jonzon (SWE), Rafael Cabrera Bello (ESP), Gareth Maybin, Scott Henry, Andrew Dodt (AUS), Richard Wallis, Peter Erofejeff (FIN), Andrew Marshall, Justin Walters (RSA), Alexandre Kaleka (FRA), Alexander Levy (FRA)
72 - Soren Hansen (DEN), Peter Hedblom (SWE), Graeme Storm, Johan Edfors (SWE), Felipe Aguilar (CHI), Thomas Bjorn (DEN), Shiv Kapur (IND), Magnus A Carlsson (SWE), Paul Waring, Matthew Nixon, Kristoffer Broberg (SWE), Scott Arnold (AUS), Phillip Price, Shiv Shankar Prasad Chowrasia (IND), Rikard Karlberg (SWE), Brooks Koepka (USA), Brett Rumford (AUS), Stephen Gallacher, Romain Wattel (FRA), Andreas Harto (DEN), Christopher Doak
73 - Francesco Molinari (ITA), Hennie Otto (RSA), Michael Campbell (NZL), Joost Luiten (NED), Estanislao Goya (ARG), Rhys Enoch, Richard McEvoy, Danny Willett, Peter Lawrie, Jose Manuel Lara (ESP), Anthony Snobeck (FRA), Niclas Fasth (SWE), Tommy Fleetwood, Sam Little, Julien Quesne (FRA)
74 - Joakim Lagergren (SWE), Morten Orum Madsen (DEN), Scott Jamieson, Pablo Larrazabal (ESP), Prom Meesawat (THA), Alejandro Canizares (ESP), David Higgins, Bernd Wiesberger (AUT), Steve Webster, Mark Tullo (CHI), Matthew Baldwin, Chris Paisley, Gary Lockerbie, Gareth Wright, Jbe Kruger (RSA), Thorbjorn Olesen (DEN), Ignacio Garrido (ESP)
75 - Richard Bland, Richard Dinsdale, Victor Dubuisson (FRA), Matthew Southgate, Lee Slattery, Kiradech Aphibarnrat (THA), Fabrizio Zanotti (PAR), Fredrik Andersson Hed (SWE), Chris Lloyd, Thomas Levet (FRA)
76 - Mikael Lundberg (SWE), Jeev Milkha Singh (IND), Bjorn Akesson (SWE), Peter Whiteford, David Howell, Scott Strange (AUS), Simon Dyson, Seve Benson, Ricardo Gonzalez (ARG), Gary Boyd, Scott Hend (AUS), Alastair Forsyth, Lorenzo Gagli (ITA), Richard James