The South African left-hander compiled an impressive 131 not out on day one of Wellington's Plunket Shield game against Otago at the Basin Reserve yesterday.
The 27-year-old featured in two big partnerships and has helped his side reach 348 for four.
Conway was dropped on 45 at first slip shortly after lunch. But he did more than survive - he flourished.
He flashed a lot of square drives past point and was quick to swing away anything from Michael Rippon which was slightly over-tossed.
But he was patient as well and brought up his 15th first-class hundred - his second for Wellington - in a shade under five hours.
Otago actually made a bright start to the day with Nathan Smith securing two early breakthroughs with the new ball.
Veteran left-hander Luke Woodcock was guilty of playing at a delivery he could have left.
Instead he got a thick edge as far as Josh Finnie at gully, who was in the action again when opener Andrew Fletcher nicked the ball in the same direction.
The home team had slumped to 31 for two. But the bowling effort fell away after that, Volts coach Rob Walter said.
''We weren't terrible but we weren't great either,'' he said.
''We created some opportunities but they batted well. The wicket certainly did not have as much venom as we thought [when we asked them to bat].
''But I think we just did not string enough good balls together.
''It was probably a six out of 10 bowling performance from us, I guess.''
Former Otago batsman Michael Bracewell and Conway put on 188 for the third wicket.
Bracewell, who captains Wellington, seemed on track for his first Plunket Shield century since the 2014-15 season.
He played some glorious drives and looks back at the top of his game. But on 87 he got a faint edge off Rippon through to the keeper.
Jacob Duffy was economical but went unrewarded until Jimmy Neesham top-edged a pull shot for 17.
Matt Bacon and Warren Barnes made big impressions during their limited opportunities last season but struggled against the left-handers.
They got their length wrong and Conway was clinical when he got something full outside off.
Malcolm Nofal (60 not out) whacked a breezy half century and combined in an undefeated 105-run stand with Conway during the last session to help highlight an impressive day by Wellington.
In Auckland, Dane Cleaver stroked his fourth first-class hundred to help Central Districts reach 359 for nine against Auckland at stumps on day one at Eden Park Outer Oval.
Former Otago spinner Will Somerville had a heavy work load. He got through 30 overs and took two for 83.
But seamer Matt McEwan was the pick of the bowlers with two for 64 from 22 overs.
In the other game, Northern Districts is 141 for three after a rain-affected first day of its game against Canterbury at Hagley Oval.
Dean Brownlie made 77, while Fraser Sheat has two wickets.
