Ward, the 2004 Olympic champion, recovered from a second round knockdown to defeat Kovalev by the same score of 114-113 on all three judges cards after an attritional battle at Las Vegas's T-Mobile Arena.
The win saw Ward, 32, improve his unbeaten record to 31-0 with 15 knockouts.
It was defending champion Kovalev's first defeat, leaving him at 30-1 with 26 knockouts.