Rafael van der Vaart struck in the 22nd minute before Kyle Walker's brilliant free-kick 15 minutes from time sealed Spurs' victory as Harry Redknapp's men won for just the second time in 10 league games.
Tottenham return to fourth place by virtue of better goal difference than Newcastle while Chelsea - 6-1 winners over QPR earlier on Sunday - are a point behind them.
Only the top four clubs at the end of the Premier League season are due to qualify for next term's Champions League, although that number will be reduced to three if Chelsea beat Bayern Munich in this season's final.
Defeat left Rovers in the relegation zone, three points from safety, with just two games of the season left.
Source: AFP
Source: AFP