The holding midfielder capped a fine display with a magnificent free-kick into the top corner in the 73rd minute in Marseille.
However, Russia levelled with just seconds remaining when Vasili Berezutski looped a header home.
All five of our players started - Eric alongside Dele Alli, Harry Kane, Danny Rose and Kyle Walker - and England had the best of it as Wayne Rooney and Adam Lallana both went close twice. Roy Hodgson's men were particularly impressive in the first half.
Eric's free-kick gave England the lead they deserved but they couldn't see the game out as Berezutski's header in the 92nd minute found the net for 1-1.
England now take on Wales - who beat Slovakia earlier in the day - in the second group match in Lens on Thursday (2pm UK).