Latham (41) and de Grandhomme (33) took their side through to 111 for one at Hagley Oval after umpires extended play by an extra 30 minutes because a result was within sight.
Jeet Raval was bowled for 33 by Kamrul Islam about 10 minutes before the scheduled end of play, but de Grandhomme came out and hit two of the first five balls he faced for six to signal’s New Zealand’s intentions to try and complete victory inside four days. He hit two more in succession to end the game.
Bangladesh, who were dismissed for 160 in their second innings in the first test in Wellington after scoring 595 for eight, were bundled out for 173 in their second innings on Monday, setting the hosts a victory target of 109.
Neil Wagner had sparked the collapse from 92 for three to 106 for seven, with the left-armer capturing three of the four wickets to fall, including two in one over.
Taskin Ahmed (33) and Kamrul(25 not out) provided some late resistance with a 51-run ninth-wicket partnership to ensure New Zealand would need to chase in excess of 100.
Tim Southee had earlier achieved a personal milestone when he had Shakib Al Hasan caught by de Grandhomme at backward point for eight to bring up 200 test match wickets.
The 28-year-old is the fifth New Zealander to achieve the mark and is behind Richard Hadlee (431), Daniel Vettori (361), Chris Martin (233) and Chris Cairns (218) on the country’s all-time list.
After rain washed out all of the third day, New Zealand resumed their first innings on 260 for seven, still 29 runs behind Bangladesh’s 289.
Henry Nicholls, who had resumed on 56, then added 98 runs with the tail to give the hosts a first-innings lead, but got bogged down as he sought his maiden test century.
Having inched through the 90s, he charged nervously down the wicket at offspinner Mehedi Hasan and only edged the ball onto his stumps to be dismissed for 98.
Wagner was the final wicket to fall when he was run out for 26 with New Zealand on 354 and a lead of 65 runs.