Che Adams almost opened the scoring after beating Vale's defence, but was foiled by goalkeeper Chris Neal.
Vale's Anthony Grant tested George Long with a curler, but Billy Sharp broke the deadlock for the Blades with a half-volley from a Dean Hammond cross.
Sharp was a persistent threat to the Vale backline, but wasted two chances to add to his earlier strike.
Former Blades defender Rob Page's Vale, who slip to 11th, had lost just once in six games prior to his return to Bramall Lane.
Port Vale manager Rob Page told BBC Radio Stoke:
"You are never happy with a defeat. Of course, we are gutted. But it is the level of performance that we set. We have played much, much better than that.
"We haven't given a good account of ourselves today against a team that were there for the taking. Our passing was awful at times. We didn't make it too hard for them.
"I can't fault the effort in the last 20 minutes . I thought we had a right go at them, but I am really disappointed. I thought we fell below the standards we have set."
Sheffield United climbed to within four points of the League One play-off places with victory over Port Vale.