After cruising to victories against Tottenham Hotspur and Everton in their previous two outings, Newcastle were looking to claim a third successive victory when they welcomed Southampton to St James' Park.
The first half did not go according to plan though, as the Saints took a narrow lead into the break following Stuart Armstrong's 41st-minute effort.
Wilson was summoned from the bench at the interval, and he managed to restore parity within nine minutes of the restart.
The Magpies took the lead in the 79th minute courtesy of a Theo Walcott own goal before Wilson scored his second of the afternoon to wrap up all three points.
Wilson has now racked up five goals in his last three games, and he has scored eight times in the Premier League this April.
As a result, the England international has set a new record for the most Premier League goals scored in a single calendar month by a Newcastle player.
The previous record was held by Alan Shearer, who scored on seven occasions in the top flight during September 1999.
Speaking to reporters after the game, Newcastle boss Eddie Howe heaped praise on the 31-year-old for his match-winning performance.
Howe said: "He was outstanding like he has been whenever he has played this season, but he's a brilliant player to have in the squad and what an impact.
"He's always had the desire to score, it's what he lives for, the team has got him in good areas and it's his job to finish that off. I've managed him for a long time and it's great to see him get the rewards his performances deserve."
Having won eight of their last nine games, Newcastle are on the verge of bringing Champions League football to St James' Park.
With five games left to play, the Magpies are sitting in third position in the Premier League table with a nine-point cushion to ninth-placed football.
Newcastle will be looking to record a fourth consecutive victory when they play host to title-chasing Arsenal next weekend.