The Reds had won 24 home games on the bounce, which started back in January 2019 when they beat AFC Bournemouth 3-0.
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...
1. Nick Pope 9
Jurgen Klopp said that it was 'Liverpool versus Nick Pope' at times. The Golden Glove contender was outstanding again. He made a catalogue of superb saves, with those from Mo Salah and Sadio Mane the pick of the bunch.
2. Phil Bardsley 7
Stretched at times as the Reds overloaded the wide areas and continued to be tested by Robertson and Mane, but he didn't let his head drop. Much stronger performance in the second half, limiting crossing opportunities.
3. James Tarkowski 8
Led the side well yet again in the absence of Ben Mee. Had a calming influence on the rest of the back four when the going got tough. Stood the forwards up well and won the header that led to Rodriguez's equaliser.
4. Kevin Long 7
Arguably one of the centre back's best performances in his 10-and-a-bit year stay at the club. Read the game well, got himself into good defensive positions, protected his penalty area and made a superb intervention to deny Salah early on.