With the Saints already three goals ahead, Jake intercepted the ball after a mistake by Victor Wanyama in the 55th minute and fed Yannick Sagbo, who in turn fired past Artur Boruc.
There was to be no comeback from Steve Bruce’s side, though, with the Saints restoring their three-goal cushion shortly before full-time.
Simon Dawkins and Adam Smith saw their Derby County side claim a comfortable 3-0 win over Sheffield Wednesday in the Championship.
Simon started up front and played 78 minutes before being withdrawn, while full-back Adam was again among the unused substitutes.
There was a let-off for Bongani Khumalo elsewhere in the Championship, as Doncaster Rovers battled to a goalless draw with Barnsley.
Barnsley were awarded a penalty when Bongani brought down Marcus Pedersen in the area, but goalkeeper Ross Turnbull saved the spot kick from Chris O'Grady to keep his side on level terms.
The points were also shared when Queens Park Rangers visited Reading on Saturday. Benoit Assou-Ekotto played 90 minutes at left-back in the 1-1 draw, with Tom Carroll still sidelined with an ankle injury.
Grant Hall, Alex Pritchard and Ryan Mason were on the wrong end of an FA Cup upset as their Swindon Town side – seventh in League One – slumped to a 4-0 defeat to Skrill Conference Premier club Macclesfield Town in the First Round.
Grant and Alex played the full match, while Ryan was substituted with five minutes remaining.
Goalkeeper Lawrence Vigouroux again put in a good performance for Hyde as they hosted Chester in the Skrill Conference Premier, but he was unable to prevent the visitors from leaving Ewen Fields with three points after a 2-1 victory.
There was better luck for our lads on loan with clubs overseas. Yago Falque played 69 minutes of Rayo Vallecano’s 2-0 victory at Celta Vigo in La Liga, while Cristian Ceballos played his part in FC Arouca’s triumph by the same scoreline over Chaves in the Portuguese Cup, starting the game before being substituted with seven minutes remaining.
Tomislav Gomelt did not feature for Royal Antwerp in their 2-1 victory over White Star Bruxelles in Belgium.