Swansea went ahead at the Landore Training Centre after two minutes through Courtney Baker-Richardson, supplied by Jordan Garrick, who doubled the lead on 22 minutes.
Sterling, pictured, pulled a goal back from the penalty spot on 23 minutes after Shilow Tracey had been fouled.
The 19-year-old forward got his second to send the two teams in level at half-time with a fine finish.
Swansea remain fourth, five points off Liverpool, the leaders, with five matches to play.
The draw took Spurs a point above the relegation zone with four to play.
Swansea: 26 Feb v Burnley (A) PL Cup
Spurs: 2 Mar v Derby (H) PL2