Latham finished 264 not out -- a world's best for an opener carrying their bat through a completed innings -- as New Zealand were bowled out for 578, and holding a 296-run first innings lead, about an hour before stumps on the third day.
Tom Southee and Trent Boult then reduced the visitors to 20 for three at stumps, with Kusal Mendis, who is on five, and Angelo Mathews (two) to return on Tuesday to see if they can avoid an innings loss inside four days.
Despite the pace bowling fireworks towards the end of play, the third day belonged to the 26-year-old Latham.
The left-hander was concentration personified as he built on the century he completed on the Sunday and brought up his double with a controlled push into the leg side for a single.
He immediately broke into a grin as he trotted through to complete the run and become the 15th New Zealand batsman to score a test double century and first since Ross Taylor scored 290 against Australia in Perth in November, 2015.
His score is the sixth-highest for New Zealand, with Brendon McCullum's 302, on the same ground against India in 2014, still the benchmark.
It was a welcome return for Latham, whose place in the side while probably not under serious threat, had begun to be questioned after a lean run of form.
Since his last century of 177 against Bangladesh in early 2017 he has scored a total of 488 runs in 19 innings at an average of 27.11, almost 10 runs lower than his career average.
In that period he passed 50 just four times.
Latham played the anchor role to a fluent Kane Williamson on Sunday and continued to accumulate on Monday as the rest of the lineup took a more aggressive approach.
Only BJ Watling from the top seven failed to get going on a placid pitch, with Taylor and Henry Nicholls both scoring 50, while Colin de Grandhomme hit three fours and three sixes in his 49.
Jeet Raval (43) and Williamson (91) were both dismissed on Sunday.
(Reporting by Greg Stutchbury; Editing by Amlan Chakraborty)
