Saints are now one place and one point above the relegation zone and realistically need three more wins (they only managed five in 30 games this season under Pellegrino) to stay out of the bottom three.
Southampton are hoping to have Pellegrino's successor in place for Sunday's FA Cup quarter-final against Wigan Athletic.
Former Watford boss Marco Silva instantly emerged as the frontrunner to succeed the Argentine on Monday night.
The Welshman was sacked by Stoke in January after four-and-a-half years, having previously managed Wales, Blackburn, Manchester City, Fulham and QPR.
Former team-mate and arguably the club's greatest ever player Matt Le Tissier believes Hughes has what it takes to save Southampton from dropping into the Championship.
The club sit 17th in the league on 28 points, a point ahead of Crystal Palace and Stoke, with eight games left to play.
"I feel so sorry to leave the club in this situation, but when you don't get results I understand the decision the club has to take", he said.
Southampton, who are the ninth Premier League club to change manager this term, are in their sixth straight season in the top flight and have not finished lower than 14th in that time.
Southampton have won only 1 of their last 17 matches, and their most recent outing was an incredibly underwhelming, 3-0 defeat to Newcastle United at St. James's Park.
Of this season's contrasting fortunes, Pellegrino said: "We have been living a hard season for many reasons".
The Frenchman had guided the Saints to the league cup final (their first appearance in a final for 14 years) and eighth place in the Premier League, not a bad balance sheet after one season in charge.