The captain Tendulkar and Rayudu each made 51 as Mumbai scored 159 for five before stopping Punjab at 136 for eight for their sixth victory in eight matches of the Twenty20 tournament.
Mumbai now lead the 10-team league table with 12 points.
Shaun Marsh, the Australian batsman, top-scored with a 47-ball 61 for Punjab, who suffered their fourth defeat in seven games. He put on 72 for the second wicket with Paul Valthaty, who contributed a 38-ball 33.
Pacemen Lasith Malinga and Munaf Patel, and the off-spinner Harbhajan Singh bagged two wickets apiece for Mumbai.
Tendulkar and Rayudu earlier propped up the innings after Mumbai had lost South African Davy Jacobs (10) in the third over, adding 95 for the second wicket.
Rayudu, who hit the seamer Praveen Kumar for two fours and a six in the same over, was the first to reach half-century with a boundary off leg-spinner Piyush Chawla.
He fell in the same over while attempting another big shot, caught superbly by Dinesh Karthik at deep midwicket after hitting one six and eight fours in his 37-ball knock.
Tendulkar, who hit left-arm spinner Bhargav Bhatt over deep square-leg for the first six of the innings, also fell soon after completing his half-century. He cracked one six and three fours in his 45-ball knock.
West Indies batsman Kieron Pollard smashed two sixes in his 11-ball 20 and Rohit Sharma hit a brisk 18 to help Mumbai cross the 150-mark.
Australian paceman Ryan Harris and Chawla each bagged two wickets.