McSweeney and Liam Scott (52no) took Australia A to 4-241 at stumps on day two after the visitors made 272 when asked to bat first at Marrara Oval.
The pair had added 114 for the fifth wicket, putting their side in a prime position to push for victory in the first of two four-day games between the two sides in Darwin.
McSweeney was called up to the Test side for last summer's home series against India, but was dropped after averaging 14.4 through the first three matches.
The 26-year-old then went on Australia's tour of Sri Lanka but wasn't used, and was not chosen in the country's squads for last month's World Test Championship final at Lord's and the current tour of the West Indies.
But after making 85 not out, five and nine in Australia A's 2-1 victory over Sri Lanka A in the Darwin one-day series that finished last week, McSweeney was back in strong form on Monday in drawing within six runs of a century by stumps.
The South Australia captain had turned in a composed knock against the Sri Lanka A attack, with six fours coming in his 219-ball stay at the crease.
His SA teammate Scott was in fine touch as well, the pace-bowling allrounder reaching 52 off 117 balls with four boundaries.
The pair steadied the ship after Australia A lost their third and fourth wickets with the score on 127, with Kurtis Patterson (19) lbw and captain Jason Sangha caught out for a three-ball duck.
Both wickets were taken by 24-year-old left-arm spinner Sonal Dinusha (2-44), who followed his strong work with the bat in making an unbeaten 105 on Sunday.
Earlier, Tasmania's Jake Weatherald struck a fine 98-ball 54 with six fours and a six, while fellow opener Campbell Kellaway of Victoria made 13.
