The tall left-hander dropped anchor and posted an undefeated 128 to help the visitors post 410 and a colossal 322-run first-innings lead.
The 32-year-old brought up the milestone with a straight drive, which would have gone for a boundary had it not hit the stumps.
He punched the air with delight as he ran through to complete the ton and later picked up the only Otago wicket to fall.
"Every 100 is special," Yovich said.
"But it is pretty pleasing to get the season off to a good start and it sets up the benchmark. There has been a lot of hard work go in over the winter."
Otago fought back, reaching 165 for one thanks to some attacking batting by Craig Cumming and Leighton Morgan.
The pair added 139 for the opening wicket and Cumming went into the sheds nine runs shy of his 16th first-class 100.
But the way he is batting, it should be a formality this morning.
Unfortunately for Otago, the damage had been done earlier in the day with Northern's lower order piling on 180 runs in an extended morning session.
Useful tail end batsmen Graeme Aldridge and Bradley Scott featured in punishing partnerships with Yovich as the visitors took a cast-iron grip on the Plunket Shield fixture.
Aldridge and Yovich added 99 for the eighth wicket, and Scott and Yovich set a new ninth-wicket partnership against Otago, scoring 112.
You would think only a determined batting display and perhaps some intervention from the weather gods could save Otago from an outright defeat.
If Northern can remove Cumming or Greg Todd, it will have the chance to exploit what is an inexperienced middle order.
Northern resumed on 195 for six, with Yovich on 47 and Anton Devcich on 9.
Devcich lasted just a further four balls and failed to add to his overnight score.
He burst out of the blocks looking for a quick single that was never there and slipped when he attempted a rapid about-turn.
Anthony Bullick ran in from cover and hit the stumps with an under-arm throw.
Aldridge brought up his fourth first-class 50 with a sparkling drive through the covers off Neil Wagner.
The bowler retaliated with a superb bouncer, which Aldridge fended through to the keeper.
Scott took up where Aldridge left off.
Having claimed his 150th first-class wicket when he bowled Shaun Haig for a duck, the left-hander whacked one six and seven fours on his way to posting his sixth first-class century.
Nick Beard was easily the pick of the Otago bowlers.
The left-arm spinner wrapped up Northern's innings when he trapped Brent Arnel in front and finished with figures of three for 59 from 28.5 overs.
Mat Harvie almost reached a dubious milestone by conceding 100 runs.
His 18 overs cost 94 runs, but he gained the prized scalp of Black Cap Daniel Flynn.
Cumming had a slice of luck on 80 when an inside edge narrowly missed leg stump.
Earlier, he had treated part-time off-spinner Kane Williamson with contempt, smashing him for two sixes and a four.
In Napier, Andrew de Boorder's maiden first-class century enabled Auckland to retain control at the midway point of its Plunket Shield match with Central Districts at a run-laden, though damp, Nelson Park, NZPA reported.
At the close of a significantly weather-affected day in which only 49 overs were possible, Central Districts were 84 for three, still 320 short of securing first innings points.
De Boorder, born in nearby Hastings, posted 14 boundaries in his ton and brought up three figures in 208 balls as Auckland improved on its overnight score of 319 for six.
The 21-year-old was ultimately stranded on 125 as Auckland lost its last three wickets for a solitary run but still compiled 403.
At the Basin Reserve, Wellington whittled away Canterbury's prospects of claiming first innings points as a weather-affected Plunket Shield match headed for a tense interlude.
Seeking 215 for first innings points, Canterbury was a precarious 139 for six at stumps of a frustrating day that saw only 41.4 overs bowled.
The New Zealand A side to play Pakistan in a three-day warm-up match in Queenstown next week will be named on Sunday.
