Smith hit an unbeaten 87 off 58 balls with 10 fours and three sixes while Tendulkar scored 58 off 51 balls with six boundaries.
However, both batsmen got some reprieve from sloppy Royals fielding, who dropped Smith twice and Shane Watson could not hold onto Tendulkar's top edged sweep at backward square leg.
The Mumbai Indians finished third in the standings with 20 points and will take on the Chennai Super Kings in the eliminator on Wednesday.
The Delhi Daredevils will meet the Kolkata Knight Riders in Pune on Tuesday and the winner will qualify for the final. The loser will take on the winner of the Mumbai Indians v Chennai Super Kings game in Chennai to qualify for the May 27 final - also at Chennai.