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 said of the result on Sky Sports 2. "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 Adkins.
However, Rodriguez said: "I only had eyes on the ball. I didn't see the keeper to be honest until it went in."