Bumrah, who has two overs in hand, comes back into the attack to bowl the 48th over.
Richardson clips it uppishly on the leg side for two runs as Dhawan is slow to get to the ball.
He opens the face of the bat and runs it fine past a diving wicketkeeper Pant for a four.
Bumrah overpitches as Richardson drills it through the covers for another four to take Australia past the 250-run mark.
Bumrah bowls a good yorker which Richardson digs it out and looks for a quick single but goes back. An angry Bumrah throws down the stumps at the batting end and ends up conceding four overthrows.
The next ball is a full toss which Richardson drives down the ground as Bumrah gets his shoes to stop it and give away just one.
Cummins then makes room and steers a wide delivery from Bumrah through the vacant thirdman region for a four as the fast bowler goes for 19 runs in his ninth over.
Bumrah has conceded just 14 runs from his first eight overs, but ended up giving away more than in his ninth over.
Bhuvneshwar makes the breakthrough to end an irritating partnership for the Indians with the wicket of Cummins, who gets an inside edge which goes off the boots and is caught by the bowler for 15.
A good final over from Bumrah as he concedes five while picking up a wicket to finish with good figures of three for 48 in 10 overs.
Despite going for runs in his previous over, Bumrah continues as he comes in to bowl the final over of the innings.
He foxes Richardson two balls in a row with good change of pace. The right-hander finally gets some bat on ball as he lofts it on the leg side for a single to deep midwicket.
Lyon steals a quick bye after he is beaten to bring Richardson back on strike, who then gets a thick outside edge which goes over short thirdman for a four.
Richardson is run out off the last ball going for an impossible second run after a good innings of 29 from 21 balls as Australia finish on 272 for nine in their 50 overs.