After Cliff Byrne had cancelled out Max Gradel's opener for the visitors, the game turned into a midfield slog until Howson, United's 22-year-old homegrown midfielder, took the firmest of grips on the tie.
One of just three starting survivors from Leeds last visit to Glanford Park in August 2008, Howson scored with his right foot, his left foot and his head as Simon Grayson's men returned to form after a run of one win in five.
Grayson made three changes to the side that were thrashed 4-0 by Cardiff on Monday, and it eventually proved to be enough as Scunthorpe were unable to live with them, meaning their wait to beat Leeds will go into a 50th year.
Cardiff's first goal in that 4-0 win came after a collision between Kasper Schmeichel and Alex Bruce, and the duo almost shipped another goal in identical circumstances after just two minutes, but debutant Andy O'Brien was on hand to clear off the line from Chris Dagnall.
Leeds made the most of their let-off too and took the lead after eight minutes through Gradel's first of the season.
The Ivorian, back in the side at the expense of Davide Somma, drove home low across Tony Warner's goal after a neat ball into him from Howson.
The goal was Leeds' only real opportunity in the early exchanges, though, and Scunthorpe managed to build enough pressure to earn them a 27th-minute equaliser.
Good work from loanee Freddie Sears earned them a corner, and from Michael O'Connor's ball in, Byrne got up at the back post to bury a header beyond Schmeichel, although Leeds felt O'Brien had been impeded in the process.
Warner, a former Leeds keeper, then tipped an Amdy Faye header away moments before the end of the first half.
Neil Kilkenny drove over the bar for Leeds after the restart as both sides looked for a way to take a firm hold of the game, and Leeds managed to do that as the clock reached the hour mark.
Grayson's decision to withdraw the poor Faye energised the Whites, and not long after Paul Connolly's cross went through the area to the back post, where Howson was waiting to crash home a third of the season.
At the other end, Schmeichel had to tip a Sears drive over the bar, but Leeds were in total command by this point and Howson underlined that with his second, a back-post header after a Gradel cross.
That came in the 74th minute and, just as Scunthorpe were recovering from that blow, Luciano Becchio played Howson through on goal a minute later and he duly completed a maiden career treble.