The tourists declared after reaching an imposing 507-8 and then reduced Kent to 203-5 at stumps after Johnson took a wicket with his fourth ball of the match.
However, the Aussies were held up by a fine innings from former England batsman Rob Key, who made 87 before falling to Fawad Ahmed.
Australia began the second day on 348-3 with Smith on 71 not out after he had looked assured on Thursday.
And the world???s top-ranked Test batsman, who played for Kent 2nd XI in 2007, eased to a 19th first class century, which came from 152 balls, adding a couple more big blows before deciding to retire on 111.
Young Kent seamer Matt Hunn (5-99), who took three wickets on day one, then had Shane Watson (21) brilliantly caught at point by Joe Denly.
And the 21-year-old bowler???s dream match continued when he knocked out Mitchell Marsh???s off stump after the all-rounder had made a breezy 30 from 26 balls.
Wicketkeeper Brad Haddin made 35 before he fell after lunch, caught at slip by Adam Ball off Adam Riley after he had added 60 for the seventh wicket with Johnson.
And the Aussies called a halt to their innings when Ryan Harris (nine) was caught behind off Ball, Johnson finishing unbeaten on 32.
The left-armer then took 3-42 with the ball, starting the innings with a bang as he trapped Daniel Bell-Drummond lbw for a duck with an inswinger.
Key and Denley (36) then put together a second-wicket stand of 81, before Peter Siddle (1-32) had Denly caught behind by Haddin.
And Kent skipper Sam Northeast (25) helped Key to add a further 59, only to fall when he edged to Haddin as he tried to leave a dangerous Johnson delivery.
Key was batting smoothly at the other end and took a liking to Ahmed (1-59), hitting the leg-spinner for three fours in five balls.
However, he looked for another boundary off the final ball of the over, only to be caught by a diving Shaun Marsh in the mid-wicket region.
The ever-dangerous Johnson then bowled Ben Harmison (five) but Sam Billings (24 not out) and Adam Ball (21 not out) put on 35 as they guided Kent to stumps, which came with the hosts still trailing by 304.