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 to push former manager Nigel Adkins closer to the drop.
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."
While Reading's 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."
The defeat leaves Reading in a desperate situation but Adkins insisted he would stay positive.
"We needed a win today," he said. "We were up against a good team but we're at home and we've got to win the game of football. We've not done that, that's the reality of where we are. We've got to keep working hard."
Reading were left to rue a glaring miss by the usually reliable Adam Le Fondre when the game was still goalless, but Adkins was not pointing a finger of blame.
"He's a great goalscorer in my eyes, a great finisher," he said. "We've got him on the field for that reason so when the opportunity comes he can take it. It didn't happen today but it will in the future."
On Rodriguez's goal, he added: "Maybe somewhere else on the field of play, his foot was very high so he could very easily have given us a free-kick. It's pivotal because it puts them 1-0 up and I thought we were doing okay in the first half."
Reading now have six games to somehow overhaul a number of clubs if they are to play Premier League football next season.
"It's a situation we don't want to be in, but we're in it," Adkins said. "You can hide away or you can face up to the reality of it."