Mumba and Whittaker struck in the second half to help propel Argyle to the top of the table.
Freddie Ladapo's goal gave the Tractor Boys a half-time lead.
Mumba's 69th-minute stunner brought the home side level and turned the tide of the match before Whittaker's shot into the top corner finished the comeback.
In the final minutes of the match, Christian Walton hit the bar with a headed corner.
The league's best home and away records were put to the test against each other.
When Ladapo's shot cannoned up off Dan Scarr and over Michael Cooper to give the away side the lead, it looked like they were going to extend their perfect start to the season.
Marcus Harness and Sam Morsy both escaped with yellow cards at the end of the half as they were the only two players who had played in the game.
The away side started the second half looking to add to their tally, with on-loan Argyle defender.
Mumba drilled home through a crowded penalty area in Home Park.
After making a fine save to turn Whittaker's left-foot strike around the post, he was powerless to stop the attacker from smashing another shot at the goal, which flew into the top corner.
In the last minute of injury time, after a corner was won, the goalkeeper rose high to meet the ball and send it crashing against the bar.
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