The 31-year-old dropped her rival with a left to the ribs in the second round.
Sanchez, who could not retain her title after failing to make weight, survived but took heavy blows to the head.
Despite sporting a cut above her right eye late on, Taylor stood firm to win 99-90 on all of the judges' cards and take the WBA lightweight title.
Taylor was embraced by family members when the cards were read and, with the Principality Stadium almost full ahead of Anthony Joshua's meeting with Carlos Takam, the decision was met with a big roar.
She had labelled this the biggest night of her life, a big claim for a five-time world amateur champion and the 2012 Olympic gold medal winner.
But the Bray fighter never looked in danger of suffering stage fright. She strutted into the ring with confidence and started quickly, landing several right hands in the opening two-minute round.
Sanchez, who was beaten for only the third time in 20 fights, could not shift a solitary pound despite being given two hours to do so after Friday's weigh-in.
It meant only Taylor could leave Wales with the title, but the Buenos Aires fighter still found the grit needed to rise from a crippling blow to the body in the second round.
The Argentine brought a threat of her own, landing some stinging counter punches as Taylor applied consistent pressure in a contest packed with the kind of heavy hitting which draws gasps from those in attendance.
But two rapid-fire right hands in the fifth summed up all that Taylor was about as she maintained exquisite accuracy, notably with the right hand.
The cut above her eye failed to deter her late on as a five-shot combination found the target in the ninth. She was simply quicker to the punch and, when the pair boxed at close quarters, Taylor always looked more willing to walk through punches and be the last of the two swinging.
With a world title to her name she now carries significant collateral in chasing unification bouts or pursuing a mooted clash with UFC start Holly Holm, herself a former world boxing champion at multiple weights.
Taylor will have options, but once again showed how comfortable she is on the big stage as she completed her rapid ascent to the top of the pro game and built on a glorious amateur pedigree. THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>