Canterbury resumed at 36 for two and was dismissed for 199 on a bowler-friendly surface at the University Oval.
Young was a standout with an undefeated 103 and Otago was 68 for two when bad light brought an early end to play just after 6pm.
Ian Butler bowled superbly to take three for 53 from 19 overs, and James McMillan was a handful when he got it right, finishing with four for 51 from 17 overs.
But neither of them could find a way past Young's broad bat.
The Canterbury wicketkeeper-batsman scored more than half his team's total. He swivelled into pull shots at every opportunity, profiting heavily from the stroke.
He flicked a short delivery from McMillan over third man for six and also played a memorable on drive which whistled off his bat on the way to the rope.
His 50 was raised during the lunch break when the umpires corrected a call from four leg byes to four runs.
Just as well for the batsman otherwise he would have been left stranded on 99.
Willie Lonsdale did a fine job compiling zero in an almost 40-minute stay to help his team-mate get through to his century.
He folded shortly after Young swatted a Butler delivery to the mid-wicket boundary to raise his eighth first-class hundred.
Dean Brownlie's dress rehearsal for the third test against South Africa in Wellington later this week did not go well at all.
He was bowled for nought but it did take a fantastic ball from Butler which swung in and then nipped in some more from the pitch.
Still, it was an awkward six-ball stay in which he was struck by Neil Wagner and never looked comfortable.
Butler, who has been sidelined with an injury and has missed the last two games, made a successful return. He bowled with great control.
His line and length was pretty near impeccable and he got good shape and plenty of assistance from the wicket.
He dismissed Peter Fulton on Sunday and added Black Caps Brownlie and Andrew Ellis to his tally.
McMillan did not appear to always be on song but his ability to generate a little bit of extra pace from the pitch aided his cause.
The home side's reply suffered an early setback with Craig Cumming out in the seventh over for 13.
He lost sight of the ball and ended up guiding it gently into the slips, and Michael Bracewell was undone on 10.
Otago will resume with Hamish Rutherford undefeated on 29 and Neil Broom on 6.
There are still two days remaining so an outright result is not out of the question despite most of the first day being lost to poor light and rain.
At Karori Park in Wellington, rain and bad light also affected play in the encounter between the men from the capital and Central Districts, APNZ reports.
Wellington, which resumed on 437 for six, advanced its score to 501 for six in the first session before it declared with skipper Grant Elliott unbeaten on 188.
It was a selfless gesture from the former New Zealand player who had a double century in his sights, but he chose to put the team above individual accomplishments.
Central batted for just nine balls before the rain came and an early lunch was called.
Play was officially called off for the day at 3.55pm with the visitors on 1 for none with openers Dean Robinson and Jamie How at the crease.
At least 105 overs are scheduled to be bowled on day three today, and CD will have to spend a significant amount of time in the middle to avoid being beaten.
In Auckland, no play was possible on day two of the clash between Northern Districts and Auckland, which would have been frustrating for recalled Black Cap Daniel Flynn who finished day one unbeaten on 68.
With the third test between New Zealand and South Africa due to start in Wellington on Friday, Flynn would have loved nothing more than to have the opportunity to bat for a long period at Colin Maiden Park.
Word out of the New Zealand camp has indicated that Flynn may open the batting against the Proteas' dangerous seam attack, and he could only benefit from spending more time in the middle against a strong Auckland bowling line-up.
Northern finished day one on Sunday with its score at 266 for six and it may declare overnight in a bid to move the game along heading into day three today.
