Tagoe, who joined Partizan from German side Hoffenheim in January, took his tally to six goals in four games for Partizan as the Serbian champions stretched their unbeaten run against Red Star to nine matches.
The defeat was a derby baptism of fire for Red Star's new Croatian coach Robert Prosinecki, whose decision to leave top scorer Andrija Kaludjerovic on the bench backfired straight from the kick-off for the cup holders.
Red Star missed several good chances in the first half including an Evandro effort moments before Tagoe fired the hosts ahead in the fourth minute, when he glanced Milan Smiljanic's wayward volley past Red Star keeper Sasa Stamenkovic.
Partizan goalkeeper Vladimir Stojkovic pulled off a superb save against his former club when he denied Cadu and Ivica Iliev forced Stamenkovic into a good save before Tagoe pounced again in the 49th minute.
The forward, who played in midfield for Ghana during their run to the 2010 World Cup quarter-finals, rose above his markers to head home Stefan Babovic's cross and send the Partizan end of a well-behaved crowd into raptures.
"It was a good and action-packed derby which Partizan deserved to win, although the first half was Red Star's best performance since I took over in January," Prosinecki told a news conference.
"This is a huge setback but we have to believe that we can overturn the 2-0 deficit in the return leg," said the 42-year old former Croatia midfielder, who had racked up three successive league wins with Red Star.
In the other semi-final, last year's finalists Vojvodina Novi Sad came from behind at Sloboda Point Sevojno to win 2-1 thanks to goals from Cameroonian striker Aboubakar Oumaru and Macedonian defender Danijel Mojsov.
The return legs will be played on April 6.
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