Hull supporters have long been frustrated with the ownership of Assem Allam and their protests spilled onto the pitch with 19.04 on the clock - marking the year in which the club was formed - as sponge balls were thrown onto the surface and whistles were blown.
Further whistles and chants of 'we want Allam out' came on the 30-minute mark, and the fans had little first-half action to support with Evandro coming the closest to breaking the deadlock.
Dicko forced Jamal Blackman into a fine save with a stinging drive from range, before the forward fired in from close range in the 55th minute from the the resulting corner after a neat one-two with Irvine for his 50th goal in English football.
Irvine played a full game for Hull, earning a yellow card as well as setting up Dicko's goal.
After a slow start, fine work from Dicko set Ola Aina free down and the fullback produced a driven cross for Evandro, whose initial shot was well blocked by Jack O'Connell before Blackman denied the forward at the second attempt.
United looked to hit the home side on the counter and and good link-up play between John Fleck and Billy Sharp set Chris Basham free but his strike from 20 yards was well wide.
Hull were inches from taking the lead when Seb Larsson tried to catch Blackman out at his near post with a 35-yard free-kick but his effort drifted just wide.
A moment of delay ensued as the protests began, with the home fans throwing yellow stress balls onto the playing surface, as they did during their last home televised match in October.
Sheffield United midfielder Lee Evans played an inch-perfect long pass for centre-back Basham, who made a marauding run into the Hull area and nodded to George Baldock, but he could only fire straight at Hull goalkeeper Allan McGregor.
The Blades nearly snatched the lead on the stroke of half-time when neat play between Basham and Baldock led to the latter picking out Leon Clarke in the penalty area. He cushioned a pass to Fleck who flashed a half-volley just wide of the post.
Seven minutes after restart, a hopeful long ball upfield from the visiting defence was capitalised on by Sharp as he outmuscled Angus MacDonald, however his strike was straight at McGregor.
Hull responded and forced Blackman into a full-stretch save two minutes later when Evandro laid off for Dicko to drill a shot from 25 yards, which resulted in a corner and the opening goal.
Larsson's inswinging corner was only half-cleared to Evandro on the edge of the area and his miscued strike fell into the path of Dicko who played a one-two with Irvine before scoring.
Chris Wilder's United side struggled to get a foothold in the match after that as Hull defended valiantly, while Kamil Grosicki had two chances to double the lead, failing on both occasions.
