The hosts had crumbled to 82-6 in pursuit of 287 at Trent Bridge, before a brilliant 93 from Jos Buttler gave them a chance to salvage a result.
Chris Woakes, who finished unbeaten on 95, continued the recovery but when he failed to get a Nuwan Pradeep yorker away to leave 10 required from two balls the game looked to be up.
However, Woakes and Yorkshire all-rounder Plunkett scrambled three to square-leg off the penultimate delivery as the tourists lost their focus, and Plunkett punished them with a huge swing down the ground to level the scores.
“It was nice to get that one out,” said Plunkett. “Woakesy put us in a great position and we bat all the way down.
“We scrambled that three, then hoped he’d just miss it a bit. It’s good for the team to know we bat all the way down.”
Plunkett was listed to come in at 11, but was promoted ahead of Adil Rashid with his big-hitting required.
“We bat all the way down which gives us the best chance,” he added.
“It just shows the depth we’ve got. It’s good for the team you know you can carry on all the way through the innings and if you have a wobble up top you can carry on.”