Rose, 43, played 36 holes in eight under par to tie fellow Englishman Dominic Clemons for first place at Burnham and Berrow in Somerset.
Clemons was defeated in the Amateur Championship final less than two weeks ago, which prevented him from earning an Open spot.
Rose, who tied for second in 2018 and finished fourth on his amateur debut in 1998, has participated in every Open since 2007 when healthy.
Garcia, who has finished second in the Open twice, was two strokes outside the top four at West Lancashire, exactly as he was a year ago.
The Spaniard only now qualifies for the Masters as a past champion due to his low world ranking following his move to LIV Golf.
This month in Ayrshire, the 44-year-old had hoped to compete in his 100th major, but his three-under-par total only secured him a share of sixth place.
Dan Brown joined Sam Horsfield and amateur Matthew Dodd-Berry from Royal Liverpool as the three Englishmen who ended tied for first place on six under.
Five miles from Troon, at Dundonald Links, Jack McDonald of Ayrshire won a play-off over Daniel Young, another Scot.
