Leicester, who have won four straight Premier League games and lost only one of Puel's eight in charge, are eighth in the table on 26 points, eight points clear of Southampton.
The visitors raced into a 3-0 lead inside 38 minutes as Riyad Mahrez drilled in the opener, Shinji Okazki pounced on a loose ball to double the tally and Andy King scored at the far post to give them a commanding advantage at the break.
Maya Yoshida poked the ball over the line to claw a goal back for the hosts in the second half, but Okazki scored his second with a first-time finish to ensure there was to be no comeback.
(Reporting by Toby Davis,; Editing by Ed Osmmond)
