The City striker replaced Noel Hunt in the 68th minute of the game at Croke Park in Dublin in front of a 36,000 crowd, to earn his fifth cap.
Best avoided a second yellow card and will be available for the Republic's Play-off matches next month.
Fellow Coventry City goalkeeper Keiren Westwood was an unused substitute.
A number of City supporters were at Wembley to see England beat Belarus 3-0. Peter Crouch scored twice.
Wales won 2-0 in Liechtenstein with goals from Vaughan and Ramsey.