A career-best 152 from Otago opener Aaron Redmond laid the platform for the visitors, while Sam Wells added 81 and Jimmy Neesham produced a boundary-laden 48.
Wellington off-spinner Jeetan Patel picked up 5-80 from 40.1 overs as he turned the screws on Otago.
Wellington closed day two on 33-1, still 90 runs behind with Josh Brodie and Stephen Murdoch at the crease.
In the battle for the wooden spoon at the Hagley Oval in Christchurch, Canterbury applied the blowtorch to Auckland.
The Cantabrians cobbled together 302 in their first innings in reply to Auckland's first-up effort of 173 on day one to establish a healthy lead.
Auckland were then reduced to 110-7 at the close of play on day two and still trail by 19 runs with only three second-innings wickets in hand.
Canterbury paceman Matt McEwan took 3-41 today, while Ryan McCone picked up 2-16.
Auckland skipper Gareth Hopkins finished the day unbeaten on 25 but will need to find a reliable partner tomorrow if Auckland want to bat long enough to avoid a heavy defeat.