A pair of Swedes, Patrik Sjoland (68) and Henrik Stenson (67), share third place at 8-under-par 136. A trio of Englishman - Mark Foster, Barry Lane and Simon Wakefield - are two strokes further back at minus-6.
McDowell opened on the back nine of the Duke's Course at Woburn Golf and Country Club. He birdied the par-3 11th for the second straight round, but faltered to a bogey at the next.
The Ulsterman bounced right back to birdie the 13th to move back to 6 under. McDowell ran off three straight pars before draining a birdie at the 17th. He made it two in a row as he converted a birdie try at the 18th.
Around the turn, McDowell stumbled to his second bogey of his round at the par-4 third. Again, he responded by carding a birdie at the next to get back to minus-8.
McDowell dropped another shot at the sixth, but closed in style. He birdied the par-3 eighth and also carded a birdie at the ninth to join Price atop the leaderboard.
'I made three bogeys and bounced back from them all pretty quickly which is always very satisfying,' said McDowell, who won the Telecom Italia Open earlier this year. 'I haven't controlled the golf ball the way I know I can. I haven't had it completely under control with the driver and I hit a couple of loose irons today, but all in all I have been happy with the way I have been scrambling.'
Price used a hot closing stretch to jump to the top of the leaderboard. He wrapped bogeys at three and five around a birdie at the fourth. Price birdied the 10th to get to even par for his round.
The Welshman notched back-to-back birdies from the 12th to get to 6 under but he tripped to another bogey at the 15th.
Price, a three-time winner on the European Tour, sank a birdie at the 16th for the second straight round. He made it two straight when he birdied the 17th. Price then eagled the last to play the final three holes in 4 under par.
Nick O'Hern, who shared the first-round lead with Jose Manuel Lara and McDowell, managed an even-par 72. He stands in a tie for eighth at 5-under-par 139 alongside Marcus Fraser.
Lara is one stroke further back at minus-4. He is joined there by Anders Hansen, Mattias Nilsson, Gordon Brand, Jr., Jamie Elson, Klas Eriksson, Martin Erlandsson and Ian Woosnam.
The cut fell at 1-over-par 145 with 71 players advancing to the weekend. Among those missing out on the final two rounds were European Ryder Cup performers Colin Montgomerie and Ian Poulter, who both finished at 4-over-par 148.