Although Reading began brightly and created a number of openings, Rodriguez got the first in the 34th minute and Adam Lallana made sure of the win 18 minutes from time.
The win lifts Southampton seven points clear of the drop zone, while Reading are seven points adrift of safety at the foot of the table.
"It's massive," Rodriguez told Sky Sports. "Every game we're coming to now is a big game and we just need to carry on working hard and improving to the end of the season.
"Reading put us under pressure and played really well but the timing of our goal was brilliant for us. It kicked us on."
There was a little controversy about Rodriguez's goal as he clattered in to goalkeeper Adam Federici after getting the vital touch, but no foul was given to the clear displeasure of Reading manager Nigel Adkins.
However, Rodriguez said: "I only had eyes on the ball. I didn't see the keeper to be honest until it went in."
While the decision to sack Adkins and replace him with Mauricio Pochettino in mid-season was controversial, Rodriguez is certain it is paying dividends for Southampton now.
"I think he's given us a belief," he said. "He's very passionate, he's very good in tactical situations and the team spirit is there. It's a great feeling to be on the winning side."
But he also had words of praise for former boss Adkins.
"He's a great manager," he said. "He'll do a fantastic job I'm sure at Reading but we can only concentrate on ourselves and it's a great win for us today."