Januzaj's superb second-half goal sent Belgium into a last 16 clash with Japan while England will now advance to a second round meeting with Colombia on Tuesday.
Tunisia had been woeful in the opening period, but started the second half strongly and pulled level six minutes after the restart when Fakhreddine Ben Youssef tapped in from close range after a flowing move.
A powerful header from Barcelona's Yerry Mina fired Colombia into the last 16 of the World Cup with a 1-0 win over Group H rivals Senegal, who crashed out due to a poorer disciplinary record than Japan.
Japan and Poland were booed from the pitch in Volgograd after a farcical end to their final Group H match which saw the Blue Samurai qualify for the last 16 despite a 1-0 defeat.
