McKinnon’s men secured the last available place in the next round by seeing off Championship rivals Dunfermline 2-0 with second-half goals by Simon Murray and Scott Fraser.
The Tangerines have endured a hard summer since being relegated back in early May, but McKinnon’s arrival has brought back some of the feelgood factor to the resurgent Tayside club.
The United gaffer believes his burgeoning team are prepared for the fight to regain Premiership status which begins at home to Queen of the South this weekend.
McKinnon, whose side face Partick Thistle in the next round at Tannadice, said: “It sets us up nicely for the start of the league. I think it was important for the fans to see a couple of home wins in the cup at Tannadice. We would rather be going into it with victories than defeats.
“The boys have done well considering we’ve had to change the mentality over the summer by going out and winning games.
“I think the objective was to qualify from the group and we’ve done that.
“We had to keep the tempo up because Dunfermline are a decent side.
“We need to earn every point in this league campaign.
“We’ll look forward to the Partick Thistle tie when it comes. They’re a league above us and we will show them every respect.”
On-loan Aberdeen striker Cammy Smith was suffering from a pre-match migraine so missed out but teenager Jamie Robson came in for a rare start at left-back.
Newly-promoted Dunfermline were bidding to bounce back from their midweek 5-1 drubbing by table-toppers Inverness.
But it was the home team who settled quicker and wasted no time in going for the jugular. In the fourth minute, winger Tope Obadeyi released Fraser whose whipped cross was blocked by goalkeeper David Hutton as Murray waited to pounce.
Shortly after, Dunfermline’s Rhys McCabe was guilty of a short passback which Murray latched on to, but his effort was brilliantly saved by Hutton who raced off his line to deny the hosts an early breakthrough.
In 16 minutes, Fraser went on a solo run as the Fifers’ defence backed off and his shot from outside the penalty area whistled just over the bar.
Cammy Bell had been a virtual spectator until then but he was called into action when Ben Richards-Everton rose to meet Kallum Higginbotham’s corner, and the United keeper saved comfortably from the Englishman’s header.
However, on 38 minutes, the Pars had a penalty claim turned down. United defender Lewis Toshney appeared to clip winger Joe Cardle as he entered the danger area, but referee John McKendrick waved play on.
United, though, deservedly went ahead within four minutes of the restart.
Robson’s cross from the left was nodded on by Obadeyi and Murray was on hand to head past Hutton from eight yards.
It was Murray’s fourth goal of the season so far and Obadeyi almost made it 2-0 soon after.
The former Kilmarnock attacker outpaced the Pars defender on a lung-bursting run which ended in him shooting just wide of Hutton’s far post.
United pushed for a killer second goal and sealed matters with seven minutes remaining when Fraser curled a delightful 22-yard free-kick high into the net after substitute Henri Anier had been fouled by Richards-Everton.
Allan Johnston, the Dunfermline manager said: “We know we are better than that.
“We were sloppy at times and probably never worked their keeper enough.”