Resuming on day two of the second four-day match at 4-263, Sri Lanka A fully punished rival captain Jason Sangha's decision to send them in, powering on to make 6-485 declared.
In reply, the hosts were 1-76 at stumps at the Marrara Cricket Ground on Monday, with Jake Weatherald on 45 and Kurtis Patterson 19, and with a mountain still to climb to win the series after the first match was drawn.
Australia A's former Test opener Nathan McSweeney couldn't replicate his fine 94 from game one, the South Australian falling for 12 when bowled between bat and pad by offspinner Nishan Peiris.
Rathnayake resumed on 43, and made the most of an ideal batting strip in reaching 122 off 223 balls - his side's second century following Nuwanidu Fernando's 102 on day one.
Sonal Dinusha, resuming on five, also joined the run-fest in moving to 88 off 191 deliveries, as he and Rathnayake added 170 for the fifth wicket in 53 overs.
Their stand ended when left-arm spinner Zanden Jeh lured Rathnayake into a rash clip to short midwicket where he was well caught low down by Oliver Peake.
Dinusha and Sohan de Livera continued to punish the bowlers, adding 40 runs in 14 overs before Dinusha mishit a lofted pull and was caught at mid-on by Patterson.
That gave a third wicket to unknown 22-year-old Zeh (3-132 off 43 overs), who was the pick of the eight bowlers used despite never having played top level state cricket. The Queenslander was chosen from left-field for game one as Australian officials continue their search for quality left-arm spinners.
De Livera was the fifth batter to make a half-century or more, finishing 50 not out when the declaration came.
McSweeney hit two fours in his 20 balls before being bowled between bat and pad.
Weatherald and Patterson guided the home side to stumps adding 44 without further loss.
The first unofficial "Test" finished in a draw last Wednesday, after Australia A won the one-day series 2-1.
