Le Tissier followed a penalty in the 41st minute with goals in the 66th, 69th and 84th as the Saints took a 5-0 aggregate victory over the Division Two club.
Three Premier League teams, all strugglers near the bottom of the standings, lost to lower division clubs in the second-round, second-leg matches.
Everton dominated its game, but remained winless on the season after an 88th-minute goal gave Portsmouth a 1-1 home draw and a 4-3 victory on aggregate.
Brighton of Division Two earned a 2-0 away victory and a 3-0 aggregate triumph over Leicester. Ipwsich, already down 3-0 after the first leg, was shut out again by Division One host Bolton, 1-0.
Off the field, Aston Villa striker John Fashanu has been charged with misconduct by the English Football Association for comments made in a derogatory newspaper column about French and Manchester United striker Eric Cantona. Fashanu has 14 days to respond to the charge, which could lead to a fine or suspension or both.
In his weekly column published in the Sept. 20 edition of the Sun, Fashanu accused Cantona of unsportsmanslike and "cowardly'' play, and said the Frenchman was "in need of urgent help.'' Fashanu suggested that Cantona was "guilty of a malicious, dangerous lunge'' on Neil Ruddock of Liverpool.
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