It didn't take United long to get into cruise control in the first half, scoring ten minutes in from their first attacking spell.
Cristiano Ronaldo won a free-kick in the left corner, giving Ryan Giggs the chance to whip in a trademark delivery.
Rio Ferdinand made an aggressive, diagonal run onto the cross and thumped a header well past goalkeeper Olexandr Shovkovskiy.
Before Kyiv could make much of an attempt to level the score, Wayne Rooney doubled United's lead, easily knocking in Wes Brown's low cross.
Ronaldo had created that chance too, breaking with the ball before playing in Brown and he influenced most of United's attacking play throughout the game.
Unfortunately for the Red Devils, Kyiv had their own genius in Diogo Rincon, the scorer of their first reply. His pace, power and determination had won a corner off Anderson, who found himself defending unnaturally deep for too much of the game.
Carlos Correa, whose crossing was another constant danger, swept in a deep corner which Rincon headed in, under worryingly little pressure from the United defence.
That goal opened the game up as counter-attack followed counter-attack. One of which saw John O'Shea inside Kyiv's six-yard area, the surprise of which perhaps led to his weak shot, straight at Shovkovskiy.
The Ukrainians had just one minute to thank O'Shea for his miss, before soft defending allowed Ronaldo to score the goal that his performance deserved.
Giggs ran through down the left and found Ronaldo unmarked with an excellent, dinked cross, the Portuguese heading easily into the far top corner of the goal.
United almost had their fourth five minutes into the second half, when Anderson's mis-hit volley tricked past Shovkovskiy's left hand and onto the post.
Their attacking impetus died soon after, allowing Kyiv, bossed by Rincon, to think about getting something out of the tie.
Correa curled a free-kick just past the left post and Rincon had two shots deflected wide by some brave, if unnecessarily desperate, defending.
Just as Kyiv's attacking was reaching a peak, United put the game beyond doubt, finally finishing off one of their numerous breaks in fortuitous fashion.
Carlos Tevez, who worked just as hard as Rooney and caused almost as much havoc as Ronaldo, broke down the right and had his cross blocked by a Ukrainian hand.
Referee Mr Kassai initially gave a free-kick on the edge of the area but then, after receiving persuasive advice from Tevez, consulted his assistant referee to make the decision.
A penalty was awarded and Ronaldo put away his second goal, low to the left.
Ismael Bangoura's 78th minute goal, a rifled effort from fully 20 yards out, became little more than a consolation as United strode to their third straight European win, handing Kyiv their third straight loss and leaving them with a battle just to qualify for the UEFA Cup.