Russian striker Roman Pavlyuchenko scored twice, one from a penalty shot in the 52nd minute and the other in injury time to seal the win. Croatian striker Modric added a goal in the 76th minute.
Wigan's Henri Camara scored in the 88th.
Tottenham coach Harry Redknapp, who guided Portsmouth to an FA Cup triumph last season, has lifted Spurs away from last place in the Premier League, into the fourth round of the FA Cup, and the knockout phase of the UEFA Cup since he arrived at White Hart Lanetwo months ago.
The 32 third-round games have been spread over four days with 28 on Saturday, two on Sunday and one on Monday. The four traditional powerhouses avoided each other in the draw and all meet teams from the lower divisions.
Manchester United, which is the record 11-time FA Cup winner, goes to Southampton on Sunday. Chelsea hosts Southend, Arsenal welcomes Plymouth and Liverpool visits Preston with Steven Gerrard leading the team even though he faces criminal assault and affray charges arising out of a brawl at a nightclub last Sunday.
Portsmouth begins its defense on Saturday at home to Bristol City from the second-tier League Championship.
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