Latham and Will Young's 148-run opening stand gave Conway the chance to play a positive innings, his unbeaten 99 coming off 148 balls, and he credited the opening pair for the day's dominance.
"It was special, especially considering the fact we lost the toss," he said. "The way Tommy Latham and Will Young went about their business early doors was pretty special and Tommy Latham was just outstanding to bat throughout the day. I was really grateful to bat alongside him and contribute. It was a good day all around.
"They were very positive, and just chatting to [coaches Gary Stead and Luke Ronchi] on the sideline I said, 'I want to continue that positive mindset', and look to score as much as possible, put the spinner under pressure, as well to make their seamers come back more. Luckily it paid off."
Conway's entrance in the 38th over meant he was immediately facing Bangladesh spinner Mehidy Hasan Miraz, whose second ball to the batsman was dispatched for four, before the fourth went down the ground for six.
"It was a little bit different," Conway said. "I came in facing the spinner first up - it's not normally something I'm used to but I tried to build up the courage to come down the wicket and put him over the top. Thankfully I middled it and that allowed them to push mid-on and mid-off back to alleviate a little bit of pressure."
That got Conway underway, and 52 overs later he was still standing – a tiring day's work, but perhaps not enough for a restful night's sleep.