Johnson picked up his 200th Test scalp - including the prized wicket of Kumar Sangakkara for 58 courtesy of a brilliant catch by wicketkeeper Matthew Wade - while Bird looked like he was a veteran Test bowler as Sri Lanka were skittled for just 156 in front of a big crowd of over 65,000 at the MCG.
And Australia might even fancy their chances of bettering that score by stumps, given the pitch looks to be getting better by the minute and Melbourne is drenched in sunshine.
The Australia pace attack got a bit of movement out of the pitch during the first session, but Sri Lanka were let down by a series of poor shots and Sangakkara was the only batsman to look comfortable. That was until Wade combined with Johnson (four for 63) to pull off a brilliant catch.
Bird (two for 32) had his first Test victim with the 22nd delivery of the morning when Dimuth Karunaratne (five) came forward to a ball on a good length, but was only able to edge one through to Wade behind the stumps.
The usually reliable Tillakaratne Dilshan (11) was guilty of the worst shot of the day as he attempted to hit a booming straight drive off Johnson, only to inside edge it onto his off stump to reduce Sri Lanka to 19 for two.
Peter Siddle (two for 30) made it 37 for three shortly after when Mahela Jayawardene (three) nicked one through to Wade, before Sangakkara combined with Thilan Samaraweera to take the score through to 79 for three at lunch.
Bird, who had bowled intelligently during his first stint in the morning, had his second wicket with the third ball after lunch when Samaraweera (10) lofted a short one and Angelo Matthews (15), came and went moments later as the wickets continued to tumble around Sangakkara.
A Prasanna Jayawardene (24) cameo gave Sri Lanka some hope, but when he got a ripper from Johnson and Dhammika Prasad fell the very next ball for a duck, the tourists were 134 for seven and in all sorts of trouble.
Nathan Lyon (two for 23) came in to clean up the tail with ease and Australia - with captain Michael Clarke having passed a fitness test before the start of play - will be confident of batting Sri Lanka out of the match and going on to wrap up the series.