He shared Strange Tales with the Human Torch, but he was finally getting significant attention on the cover (Jack Kirby penciled his appearance on #126, for example) - and he was also featured in that cool upper-left-hand-corner art box that Marvel created in the early '60s.
He was given 10 pages of story space (the Torch got 13 pages), and Stan Lee and Steve Ditko used it to expand their stories - and blow the minds of the readers.
These issues featured a (rare, at the time) continued story, as Strange faces his greatest enemy for the first time - the ruler of the Dark Dimension, the Dread Dormammu (which, according to the movie, is pronounced "Door-Ma'am-Moo" - so I had it right all along).
The story allows Ditko to run wild with inventive images as he creates an unearthly environment, with flat, floating spaces serving as doorways. Pathways wind with no regard to gravity or logic, creatures of all shapes and sizes thrive, and Strange must face overwhelming odds.
A couple of notes: happily, this Dormammu is human-sized, so he and Strange can go toe-to-toe and fight as equals. Years later, Dormammu was depicted as a towering giant, and he's been that ever since (mostly), including in the movie. I've never cared for it. Also, the coloring is different, as his head is enveloped in blue flames and smoke - later appearances would change it to red, which was much more effective.
Strange is faced with an impossible task - defeating the foe who once defeated his master, the Ancient One. Even with a slight assist from the lovely Clea, who makes her first appearance, he's outmatched.
The plot twist that allows Strange to survive his battle - and "win" (sorta kinda) was brilliant, and serves to show both Strange and Dormammu in a good light - making him a better hero and Dormammu a worthy villain with personality - not just a monster.
If there was any doubt that Doctor Strange belonged in the Marvel Universe, this adventure closed the deal.
One of my all-time favorites!