Brought in to replace the lacklustre Mario Goetze, the 22-year-old winger tormented Slovakia's defence with his dribbling and quick feet, creating a first-half goal for Mario Gomez and scoring himself with a superb volley in the second.
The world champions went ahead when central defender Boateng, who had been passed fit after an injury scare, connected with a clearance in the eighth minute to volley home from 25 metres for his first international goal.
The Germans then saw Mesut Ozil's weak 13th minute penalty saved but Gomez made no mistake two minutes from halftime when he tapped home a perfect cut-back from the marauding Draxler who added the third with a fine strike just past the hour mark.
"We know his capabilities. He has two magic feet and I'm happy for him that it led to a goal. He always gives for the side and I'm happy for him," Gomez said of the Vfl Wolfsburg winger, who was instructed to take on his man by Loew.
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Draxler added: "He (Loew) gave me a lot of self-confidence, trusted me and wanted me to search for a lot of one-on-ones.
"I think we were superior and well deserving of a victory. It was nice to be in front after the goal by Boateng. We could even afford not to score the penalty."
DEFLECTED VOLLEY
Comfortable with either foot, Draxler utilised his speed and intelligence to good effect throughout, helping his side pin the Slovaks in their own half for much of the opening period.
Boateng opened the scoring with a deflected volley following a corner and ran to celebrate with team doctor Hans-Wilhelm Mueller-Wohlfahrt, who helped him recover from a muscle injury sustained in their last group game with Northern Ireland.
Ozil's weak penalty, well saved by Matus Kozacik, was one of the few blemishes in an otherwise superb Germany performance.
Slovakia may have got the better of the Germans in a pre-Euro 2016 friendly but, apart from a few forays forward, they were all at sea.
Five minutes before halftime Juraj Kucka forced a flying save from Germany captain Manuel Neuer as he sent Peter Pekarik's cross toward the top corner.
Germany hit back immediately, Draxler turning Kucka inside out before squaring for Gomez to stab the ball home from close range to make it 2-0.
Slovakia were marginally better in the second half but when the excellent Draxler hooked a volley into the top corner in the 63rd minute there was no way back.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
