Mijatovic, who scored the only goal in Real's win over Juventus in last year's final, rescued his side's hopes of making further progress this year with his second-half intervention.
John Toshack's side, trailing to Andriy Shevchenko's 54th minute strike, had looked likely to face a daunting trip to Ukraine with nothing to show from the home leg. But Mijatovic rescued his team - who had missed a host of clear chances in the first half - in the 66th minute with a vicious, curling free-kick that left the Kiev goalkeeper stranded.
Shevchenko, put through by his strike partner Serhiy Rebrov, showed superb control before clipping the opening goal past Bodo Illgner. Kiev's lead lasted only 12 minutes, though.
The all-German quarter-final first leg went the way of Bayern Munich as the current runaway Bundesliga leaders beat Kaiserslautern 2-0.
Bayern, 12 points clear in the First Division, went ahead after half an hour through their Brazilian striker, Giovane Elber. They doubled their lead four minutes later with a goal from Stefan Effenberg.
However, Kaiserslautern, who managed only one shot on target all night, were better organised after the break and, despite having their Egyptian defender Hany Ramzy sent off in the 73st minute, kept the margin of defeat to 2-0.
Juventus beat Olympiakos Piraeus 2-1 in their first leg - but conceded a goal six minutes into injury time which puts their qualification for the semifinals in doubt.
The Turin team took the lead after 38 minutes courtesy of a spectacular flying volley from their Italian international striker striker, Filippo Inzaghi. The midfielder Antonio Conte added the second 11 minutes from time and Carlo Ancelotti's side appeared well placed to reach the last four for the fourth year in a row.
But, with 96 minutes on the clock, the home goalkeeper Angelo Peruzzi pulled down Alexios Alexandris in the penalty area and an 88th-minute substitute, Andreas Niniadis, coolly fired home the spot-kick to give the Greeks hope for the return leg.Reuse content