LAS VEGAS — A few days before Andre Ward and Sergey Kovalev stepped into a boxing ring here to battle it out for light heavyweight supremacy, Kovalev’s promoter said that this would be the super fight that everyone wanted between Floyd Mayweather Jr. and Manny Pacquiao but never got.

She was right.

Kovalev dominated the early rounds of this back-and-forth match, and then Ward sprang to life and came away with a close but unanimous decision victory here in Las Vegas. All three judges scored the fight 114-113 in favor of Ward.

With the victory, Ward improved his perfect record to 31-0 and made a strong case for recognition as the best pound-for-pound boxer in the world. The victory represented a resounding return to prominence for Ward, 32, who had not appeared in a marquee fight in about four years — a period marred by injury, and defined by sporadic matches and a dispute with his promoter.

“This was a beautiful thing,” Ward said after Saturday’s decision, which allowed him to take the W.B.O., W.B.A. and I.B.F. light heavyweight titles from Kovalev. “We did it, baby. It’s a lot of hardware. Surreal.”