Liechtenstein, who have only ever won two World Cup qualifiers, stunned the visitors when Martin Buechel skipped past a tackle and scored with a right-foot shot in the 15th minute.
The team from the tiny Alpine principality, backed by a modest 1,600 crowd, were on course for their first competitive win in two years until Jan Durica was left unmarked in the penalty area and headed the equaliser in the 73rd minute.
Third-placed Slovakia, who reached the last 16 of the 2010 World Cup, dropped two points they could not afford to lose as they chase Greece for second place in the group.
They have nine points, four behind the Greeks who won 1-0 in Lithuania. Liechtenstein, who drew 1-1 with Latvia in their last match, have two points.