From Matt Henry collecting his second seven-wicket haul to the battling century stand built by Latham (65no) and Kane Williamson (51), New Zealand stacked together a few of their best sessions of a series that had been escaping their grasp.
At stumps, their second innings stood at 134-2. They now hold a lead of 40 runs, after Henry picked up 7-67 on his home patch to limit the deficit.
With time no concern in a match so advanced before day three, thoughts in the home dressing room will turn to the size of lead necessary to see off the tenacious tourists.
Only twice have a team successfully chased more than 200 to win a test at Hagley: Australia’s 201-3 in 2016 and New Zealand’s 285-8 against Sri Lanka a year ago.
On that occasion, Williamson scampered through for the winning run from the final ball, ending unbeaten on 121. This year may require a similarly pivotal, if slightly less dramatic, knock from one of his teammates.
Latham tonight looked ready. Without overlooking the imperative efforts of Henry — or the latest match-changing cameo from Glenn Phillips — it would be appropriate if the test rested in his hands.
While he and Williamson batted with a level of composure to preclude any outward display of emotion, the matching half-centuries must have brought relief.
For Latham, No 28 arrived almost exactly a year since he last raised his bat, snapping a frustrating run in which he averaged 18.5 in 13 innings. A trip home — where he notched No 27 — was all the opener needed.
For Williamson, his 34th came after three previous innings this series had reaped 26 runs, reducing his average against Australia to a subpar 36.3. Coming in his 100th test, the timing was typically impeccable.
That timing deserted him only once, a late blemish that ended his stay. Before his attempted drive of Pat Cummins produced an inside edge that disrupted his stumps, Williamson had appeared to have the same touch with which he scored three tons earlier this summer.
Coming to the crease after Mitchell Starc had nicked out Will Young for the second time in as many days, Williamson twice stroked that bowler to the fence in an unusually brisk beginning.
After surviving a confident lbw shout from Josh Hazlewood and being saved by soft hands when Cummins found an edge, scoring slowed as Williamson and Latham illustrated the type of application lacking on day one.
A much more common theme on Friday was Hazlewood beating the bat. That sight largely was absent on the second afternoon, suggesting a tricky pitch was already flattening out and day three could be favourable for batting.
Latham certainly found the conditions to his liking, joining with Williamson to take eight runs off Hazlewood’s 10th over — an unremarkable number until remembering the seamer conceded only seven while snaring four wickets in six overs on the first day.
Williamson departed shortly after the 94-run first-innings deficit had been erased, a figure that would have been far more imposing without Henry and Phillips.
The seamer started by picking up nightwatchman Nathan Lyon and Mitch Marsh for a duck, completing his second five-wicket haul of the series.
Marnus Labuschagne remained to add discouraging runs with the tail and the No 3 was doing a decent job, before Phillips injected himself in an increasingly familiar fashion.
Having dismissed Alex Carey from his second ball of the test, Phillips on the stroke of lunch flung himself right at gully to grab yet another spectacular catch, removing Labuschagne for 90.
Henry wrapped up the tail to nab seven at Hagley for the second time, leaving Latham with two sessions to successfully revive his form — and his team’s fortunes.