The SSE Hydro clash, doubling as a World Boxing Super Series semi-final, saw the unbeaten 28-year-old Scot find it tough going in the early stages.
But the fight turned in the sixth round when the 26-year-old Belarussian, nicknamed 'The Beast', was dropped twice, providing the platform for a unanimous points win for Taylor - 117-109, 115-111 and 115-111.
After extending his unbeaten record to 15 fights, Taylor will now face WBA champion Regis Prograis, with the American also unbeaten in 24 fights, and boasting 20 knockouts.
Against Baranchyk, Taylor knew quickly he had a fight on his hands as the smaller man hushed the partisan crowd in the opening two rounds with some powerful punches.
But Taylor gradually worked his way into the fight. and despite a small cut emerging under his left eye and his nose being bloodied in round five, the sixth proved pivotal as he twice dropped Baranchyk to win the round 10-7.
Although the crowd roared on Taylor, Baranchyk continued to prove dangerous, leaving the home fighter to pick his shots rather than go in for the finish.
Baranchyk appeared to find a second wind in the 11th, catching Taylor on occasion who responded in kind before an engaging 12th round in which the two fighters finished the fight with an exchange in the centre of the ring.
The judges, though, saw the result clearly, with Taylor claiming a comfortable points win to hand Baranchyk his first defeat.
On the undercard, Japan's Naoya Inoue took less than two rounds to demolish Puerto Rico's Emmanuel Rodriguez to claim the IBF world bantamweight title in their World Boxing Super Series semi-final encounter.
