The visitors raced into a 2-0 lead thanks to goals from Randall Azofeifa and Bryan Ruiz, which shocked the sell-out crowd of over 34,000.
Alexander Samedov pulled a goal back for the home side, but Vasili Berezutski, who was playing his 101st game for the national team, scored an own goal to put the Central American side 3-1 in front.
A quick-fire double from Artem Dzyuba brought Russia level but Campbell, on loan to Sporting Lisbon from Arsenal, had the last laugh as his penalty in added time gave Costa Rica victory over the 2018 World Cup hosts.
(Reporting By Dmitriy Rogovitskiy; Editing by Steve Tongue)
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