Pelle exploited mistakes by Ryan Mason and Ben Davies to poke hosts Southampton in front in the 29th minute, but Erik Lamela equalised just before half-time when Eric Dier's cross hit his arm and flew past Kelvin Davis.
Pelle restored the visitors' lead with a thumping header from substitute Shane Long's cross 20 minutes into the second half, only for Nacer Chadli to level five minutes later after running onto a pass from Dier.
Tottenham head coach Mauricio Pochettino, making his first return to St Mary's since leaving Southampton last year, saw his side move a point above Liverpool and into fifth place in the table.
Southampton also stole above Liverpool, on goal difference, but Brendan Rodgers's side now have two games in hand on both Southampton and Spurs, starting with a trip to West Bromwich Albion later on Saturday.
The teams finishing fifth and sixth will qualify for the Europa League, while victory for Arsenal over Aston Villa in the FA Cup final would also send the team finishing seventh into Europe's second-tier competition.
Defending champions Manchester City can climb above Arsenal and Manchester United to second place if they win at home to FA Cup finalists Villa. Arsenal host leaders Chelsea on Sunday, while United travel to Everton.
Elsewhere on Saturday, third-bottom Leicester City go in search of a fourth consecutive win away to bottom club Burnley in a potentially pivotal relegation tussle. – AFP
Original source: Spurs, Saints share the spoils