That proved to be the final piece of goal-mouth action in the half as England ended their World Cup preparations on a high.
Alexander-Arnold was handed his senior team debut after an impressive campaign at Liverpool which culminated in a Champions League final appearance two weeks ago.
It was just reward for a fine first-half performance but England lost some of their rhythm after the break, as Southgate made a number of changes, including handing goalkeeper Nick Pope his first taste of global football.
Los Ticos are no pushovers, however, and you can expect some fierce resistance from a side now ranked 25th in the world, who beat Northern Ireland in a 3-0 win last week during which Joel Campbell shone.
A strong first 45 minutes but a less convincing second resulted in a 2-1 win for England against Nigeria on Saturday night. Costa Rica are on offer at [9.8] while The Draw is [5.2].
Worldwide friendlies - Follow the Football match between England and Costa Rica live with Eurosport.
Rashford figures to play an important role for England in Russian Federation.
England will also host Switzerland on September 11 at a venue yet to be decided, with playing at different stadiums across the land being something that is common practice for the likes of Spain, Germany and Italy.
Until the team news is confirmed, it's hard to get involved here.
Harry Kane averages better than a goal per game under Southgate so the 4/6 (anytime) or 12/5 (first) are both options but only if he forms a two-pronged attack with Vardy and is on from the beginning.
Japan's Hiroyuki Kimura heads to Elland Road.
Whether Costa Rica field a full-strength team with Campbell, Keylor Navas, Bryan Ruiz, Marcos Urena and Celso Borges, or play some younger talents like Ronald Matarrita, Ian Smith or Francisco Valco who are yet to be seen.