The Reds had won 24 home games on the bounce, which started back in January 2019 when they beat AFC Bournemouth 3-0.
Andrew Robertson gave Jurgen Klopp's side the lead in the 34th minute with a peach of a header from Fabinho's diagonal.
But Rodriguez rescued a point with just over 20 minutes remaining when he fired James Tarkowski's header past Alisson.
Here are the ratings from the 1-1 draw in Merseyside...
But Rodriguez rescued a point with just over 20 minutes remaining when he fired James Tarkowski's header past Alisson.