A drab first half was memorable only for Southwood's stunning saves to deny long-range efforts from Siriki Dembele and Ollie Norburn.
Reading improved after the break, with John Swift firing in his seventh goal of the season and Tom Dele-Bashiru making it 2-0 with his first for the club.
Although Nathan Thompson reduced the gap with a far-post header, Dele-Bashiru secured the home win with his second near the end.
It ended a four-match winless run for Reading, with Southwood making only his second league appearance for the club.
"Luke had a very good game and, with the team's performance overall, that made him feel safe and secure," Paunovic said.
"His interventions in a couple of moments in the first half, and him also being calm and composed on the ball, gave us time and a chance to build a momentum."
Southwood replaced regular keeper Rafael, who missed the game with a broken hand.
But Paunovic declined to confirm reports that Rafael sustained the injury when punching a tactics board in frustration after the 3-3 home draw with QPR on Saturday.
"Rafael has an injury but we won today and move on, that's the most important thing," the Serb said.
"He has been assessed and, after we scanned him, the news is positive. There is no fracture, his wrist is just swollen."
On the win over Peterborough, Paunovic added: "We had a good whole game. We were always making progress to the final third, towards their box.
"After half-time, we got that edge to push forward with also the conviction to open the scoreboard."
Peterborough suffered their fourth Championship defeat in a row.
"My reaction is obviously one of disappointment," Posh manager Darren Ferguson said.
"We were well in the game and I thought that we were the better team until around the hour mark.
"Our biggest problem at the moment, anyone can see, is that we have this terrible habit of when we concede, we then concede again so quickly after.
"It makes it so difficult for us, especially away from home. And that's happened now three times out of four. It's a big problem. It's something that I need to root out somehow.
"You'd have to ask the players why it keeps happening. I can only stand on the touchline. I just know that, factually, we're losing too many goals straight after one. And that's the big problem.
"Our shape was good, on the ball and off it. We grew into the game and their goalkeeper made two very good saves."