Rajasthan had briefly moved to second position after their thumping win over Sunrisers Hyderabad Thursday. But after restricting the Warriors to just 112 for eight, Mumbai scored 116 for five in 18.5 overs and secured all two points.
Chennai Super Kings still lead with 20 points with Mumbai and Rajasthan hot on their heels two points behind.
Mumbai made the worse possible start to the chase, losing West Indian opener Dwayne Smith (0) in the first ball.
Sachin Tendulkar looked in good touch, hitting three boundaries, before he was dismissed by Mendis for 15 runs.
Dinesh Karthik (17), recalled to the national setup, failed to get going and fell prey to Yuvraj Singh's innocuous left-arm spin.
Captain Rohit Sharma (37) and Ambati Rayudu (26) held their nerves and slowly but surely edged their way towards the target.
Glenn Maxwell (13 n.o), who was bought for a whopping $1 million by Mumbai, playing his first match in the tournament provided the finishing touches with a couple of lusty blows.
Earlier, Pune lost both openers Robin Uthappa (11) and Aaron Finch (10) cheaply.
Manish Pandey (29) and Yuvraj (33) together forged the best partnership of the innings adding 59 runs for the third wicket.
However, it was all downhill from thereon in for Pune, as they lost six wickets for just 29 runs.
Mitchell Johnson, Abu Nechim and Lasith Malinga all bowled impressively, taking two wickets each while Harbhajan Singh picked up one.