The 24-year-old, who missed out in a play-off last year, was one shot behind American winner Brooks Koepka.
Another Englishman Richard McEvoy, Northern Ireland’s Gareth Maybin and Scotsman Scott Jamieson also qualified.
Europe’s 2014 Ryder Cup captain Paul McGinley and predecessor Jose Maria Olazabal failed to make it.
The 23-year-old Koepka carded rounds of 69 and 65 to book his spot at Muirfield next month, while his playing partner took second place in the 36-hole event, following his morning 70 with an afternoon 65 round Sunningdale’s Old Course.
The winner’s day began with a 06:30 BST flight from Scotland, less than 12 hours after earning his European Tour card with a third Challenge Tour win of the season in the Highlands at Spey Valley.
Maybin and McEvoy finished a further stroke behind Fisher on three under, along with fellow qualifiers France’s Gregory Bourdy and Spain’s Alvaro Quiros.
Glaswegian Jamieson was on the same two-under mark as veteran Swede Niclas Fasth.
