Pardew was Saints boss for just over a year and led the club to the Johnstone's Paint Trophy title, but says he was ''treated harshly'' and exited the club after just 13 months.
The 51-year-old made his return to Southampton for the first time this afternoon, although back-to-back promotions means the hosts are a much different proposition to the League One club he left behind 27 months ago.
Adkins oversaw that spell of success and, after his position came under early-season scrutiny, oversaw a second successive win today.
Newcastle were unable to find a response, meaning they have won just one of their eight Barclays Premier League matches since Pardew was awarded an eight-year deal, as Saints earned a first clean sheet of the season and three points to propel them out of the relegation zone.
The hosts named an unchanged side from the one that won 3-1 at QPR for today's game, while the Magpies named six of the side that played against Maritimo in the Europa League on Thursday.
Demba Ba was one of those returning and nodded wide inside five minutes, before Saints began to make an impression on proceedings.
Lallana directed a wayward Nathaniel Clyne effort just wide in the seventh minute, before Ramirez and Puncheon were denied.
Southampton were looking shaky at the back, though, and goalkeeper Paulo Gazzaniga was fortunate to see a clearance blocked by Ba come to no harm.
Opposite number Tim Krul was looking more assured and sprinted off his line to stop Rickie Lambert connecting with a misplaced Cheick Tiote pass.
The Netherlands international was once again called into action to deny a 25-yard Ramirez free-kick, before then thwarting Puncheon from a Lambert cutback.
Saints were getting closer, though, and, after an expertly-struck Lambert free-kick rattled the crossbar, they took a 34th-minute lead.
Krul rushed off his line to stop Puncheon down the right, but his clearance only found Clyne. The right-back's long shot was headed away by Saints academy graduate Mike Williamson, but Ramirez collected the ball and squared for Lallana to score from close range.
Steven Taylor denied Southampton a second goal three minutes later by blocking a goalbound Morgan Schneiderlin drive, before Williamson was booked as half-time approached.
Sammy Ameobi replaced Shane Ferguson when the match resumed, with Newcastle looking reinvigorated.
Ba headed straight at Gazzaniga from a corner, before the Southampton goalkeeper did excellently to deny Anita in a one-on-one as the Magpies continued to threaten.
They did, though, look susceptible on the break and Saints would have capitalised on that weakness but for Krul's quick reactions preventing Lallana.
Adkins' side did get the second goal they craved in the 60th minute after an excellent one-two between Puncheon and Lallana saw the latter put in a cross that Krul parried into the path of Ramirez to fire home.
Referee Martin Atkinson waved away Saints' penalty appeals five minutes later when Ramirez appeared to be brought down by Tiote, who soon came close at the other end with a curled effort.
Puncheon hit the post as Saints pushed to extend their lead but Gazzaniga had to launch himself across goal at the other end to deny Davide Santon with an excellent one-handed save.
Krul denied substitute Steven Davis at his near post when Saints returned to the attack, with Fonte then hitting the bar before Lallana was denied.
Substitute Jay Rodriguez had a goal chalked off for offside late on, before Papiss Cisse saw an audacious effort go just wide as Saints held on for a 2-0 victory.