Resuming after a rain delay on day two at Queen's, world no. 482 Golding defied the odds to keep pace with Baker in the first set.
British number three Baker came in to his own during the tie-break, however, which he won 7-1.
Golding then had an argument with the umpire following a dubious line call at the start of the second set and went on to trail 0-4.
He rallied momentarily, but Baker eased home to record a 7-6 (7/1) 6-3 win.
Baker, ranked 203 in the world, has played Tsonga once before in Lanzarote five years ago when the world number five won easily in straight sets.