The Reds appeared to be easing to victory at St Mary’s heading into the final seven minutes with a two-goal cushion.
That advantage was cut in half when Adrian hammered a clearance into former Liverpool forward Danny Ings and watched the ball sail into his net.
Buoyed by that lifeline, the Saints pushed hard for a late leveller.
They were to be left disappointed, with Jurgen Klop’s side hanging on to drag themselves over the line.
Oxalde-Chamberlain told BBC Sport on a nervy finish to a 2-1 win which could have been avoided: "I think we were in control of the game and then you concede a goal and momentum flips like that.
"It will happen from time to time and we managed to withstand that. You've got to ride your luck at times and it was really solid and a good three points."
Liverpool headed to the south coast on the back of having been taken to penalties by Chelsea in a midweek UEFA Super Cup clash.
Tired bodies and minds were inevitable, but Oxlade-Chamberlain insists the Reds were eager to avoid any post-match excuses.
He added on a game ultimately settled by goals from Sadio Mane and Roberto Firmino: "There were moments in the game where we suffered and knew we had to improve. We knew we would come under the cosh and had to withstand that. But despite playing 120 minutes and all the travel, we were never going to use that as an excuse.
"We had to turn up today and prove we were raring to go and I think we did that."
Oxlade-Chamberlain took in his first Premier League start for 16 months in a meeting with his former club, with the England international now back to full match fitness after a lengthy spell on the sidelines with a serious knee injury.
The 26-year-old said on being back in a starting XI: "The main thing is the three points for the team, whether I'm on the pitch or not. But on a personal level it is great to be back out there and contributing to a good solid performance.
"That's what you miss. I've been working hard to get back to this point, I've had iffy moments along the way, but I have to keep reminding myself it is a long journey back to where I want to be."