Suarez scored in the 59th minute and again in extra time to seal Nacional's title
Suarez, 35, returned to his boyhood club in the summer as a free agent after leaving Atletico Madrid.
The former Liverpool and Barcelona striker scored in the 50th and the 96th minutes as Nacional won in extra time.
The Uruguayan side Liverpool are based in Montevideo and took their name from the English club because of historical cultural links between the two areas.
Suarez, Uruguay's record goalscorer, has scored six goals in 13 appearances on his return to the club he joined aged 14.
He made his professional debut for Nacional at 18, in 2005, helping them win the Uruguayan league title to earn a move to Europe with Dutch side Groningen the following season.
Since then he has gone on to win five La Liga titles and a Champions League trophy at Barcelona while he won the League Cup at Liverpool and the Premier League Golden Boot in 2013-14.
He is expected to leave Nacional in November, when his short-term contract ends before the Qatar World Cup.
-- Courtesy of BBC Sport