Richard Duffy fired Vale in front after Neil Collins headed down a corner for the defender to coolly latch onto.
Scunthorpe's Paddy Madden could have levelled later on but fired the ball over the crossbar from close range.
But Wootton's late goal rescued a point and prevented the visitors from taking their first win in eight games.
The Iron remain in 17th, a point above 18th-placed Vale who are three points above the League One relegation zone.
Scunthorpe manager Mark Robins told BBC Radio Humberside:
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"We were by no means at our best tonight but we've created enough chances to win the game.
"We gave them one shot at goal and they scored.
"The changes we made had an impact no doubt about that - I told Kyle (Wooten) to go make a name for himself which he has thankfully gone and done."

Messages posted on social media claimed the user planned to "kill as many people as possible" at Montgomery High School in Bispham on Monday, the Blackpool Gazette reported.
The planned attack was in revenge for alleged bullying, the post added.
Police confirmed officers were investigating the source and would ensure the school's safety.
The unnamed Facebook user also praised gun killers in schools in the United States and posted on the school's Facebook page: "Nobody talks to me or notices me except when they're calling me a nerd and pushing me around."
Responding to one student after the post was made, the user asked: "You think it's a joke? You'll see bullets, bodies, and blood."
Principal Tony Nicholson said in a statement to parents and carers the safety of pupils and staff was paramount.
It read: "Police have confidently reinforced the view that these online postings do not represent a credible threat. They, and we, wish to reassure our parents and the wider school community that Montgomery High School can open as normal on Monday morning."
A Lancashire Police spokesman said: "We are aware of posts on social media concerning Montgomery High School in Bispham and are investigating the source and content of these messages.
"If the matter is not resolved prior to Monday, parents, pupils, staff and the wider community should be reassured that an appropriate police response will be implemented prior to the school reopening after the Christmas holiday to ensure the safety of all."

Lance Corporal Trimaan "Harry" Dhillon stalked Alice Ruggles before fatally attacking her last October.
Her parents Sue Hills and Clive Ruggles described the moment two Northumbria Police officers knocked on their door.
Prof Ruggles said: "And then they said to us Alice has been killed. And we looked at each other and said 'It's Harry'. We knew, we knew even then."
The trial at Newcastle Crown Court heard Dhillon had become obsessed with the 24-year-old and had stalked her.
Dr Hills told of her guilt about trying to reassure her daughter on the phone two days before.
She said: "And I sort of reassured her that was ok, the police knew what was going on and that it would be all right and if she just ignored him he would ignore her.
"And I only put the phone down for 10 minutes and Emma (daughter) rang and said 'You cannot tell that to her, he's going to kill her. You have got to do something'.
"And I thought she was over-reacting so I just said 'don't be silly'.
"And so of course as soon as I saw the police I knew that's that what it was.
"And I felt such a sense of guilt for having first of all told Alice not to worry and secondly told Emma not to be silly when actually if I hadn't said that Alice might still be alive."
Prof Ruggles said he didn't think any of them, including his daughter, realised how serious the situation was despite the signs.
Her parents have set up the Alice Ruggles Trust and they said they were hoping to use that and their daughter's "vibrant personality" to make other people aware of the dangers of stalking.
They said they wanted her to be remembered for that and as "smiling and laughing and making some sort of cheeky comment."
Dhillon, 26, denied murder but was found guilty and sentenced to a minimum of 22 years.
A dramatic injury-time equaliser from teenage substitute Kyle Wootton gifted Scunthorpe a point against relegation rivals Port Vale.
[NEXT_CONCEPT]
Threats to kill pupils in a shooting at a Blackpool school are being investigated by Lancashire police.
[NEXT_CONCEPT]
The parents of a woman murdered by her ex-boyfriend have said they knew immediately he was responsible.