After a poor opening period, Wright found himself ideally placed to smash home his team's opener four minutes into the second half.
John Sweeney struck in the 76th minute to put Clyde back on level terms but Wright pounced again to grab the winner for the early pacesetters.
Berwick Rangers climbed into second place after a comfortable 2-0 triumph over a poor Albion Rovers side at Cliftonhill.
The visitors opened the scoring in the 63rd minute when Kenny O'Brien skipped round home goalkeeper Neil Parry before netting from a tight angle. In the closing stages, Neil Janczyk's poorly struck shot was converted by Scott Dalziel to double Berwick's lead.
Peterhead came from behind to win 2-1 at home to Queen's Park who remain bottom without a single point. Anthony Quinn fired the struggling visitors ahead after 24 minutes but Rory McAllister equalised and Fraser McLaren added a slick 50th-minute winner.
Elgin City and Montrose battled to an entertaining 3-3 draw at Borough Briggs. Goals from David Niven and Ross McKinnon put Elgin ahead after Bryan Deasley opened for Montrose.
Niven was then dismissed and Lloyd Young levelled. Deasley's second restored Montrose's lead but Elgin's 10 men salvaged a point thanks to Sean Crighton's 79th-minute equaliser.
A sloppy display from Stirling Albion was punished by Annan Athletic who ran out 2-0 winners at Forthbank.
David Hopkirk crossed for Ali Love to score Annan's first after six minutes. Hopkirk was then denied by a fine David Crawford save but the same player netted in the 53rd minute.