In her second match since her stunning New York triumph last month, the 18-year-old came from behind to oust the Slovenian 4-6 7-5 6-1 at Cluj on Tuesday.
Raducanu has finally been able to end the anomaly of being a grand slam champion without a win on the WTA Tour.
The world No.23 registered her first Tour victory at her fourth WTA tournament after opening round losses at Nottingham, San Diego and Indian Wells.
"It feels like a huge win, it is my first WTA Tour win which makes me very happy," Raducanu said.
"It was difficult for me but I feel to win my first WTA match does mean a lot because I was on a losing streak, so I got my first one.
"I am really pleased to have come through that today."
Raducanu announced herself on the grandest stage when she claimed the Flushing Meadows title as a qualifier last month, but the Briton then lost to Aliaksandra Sasnovich of Belarus in straight sets at Indian Wells recently.
Still without a coach after parting ways with former Davis Cup player Andrew Richardson and having skipped the Kremlin Cup in Moscow, Raducanu had sought to temper the expectations but showed her class in a difficult match.
She surrendered the opening set tamely after being 4-1 up before showing glimpses of the fighting character that marked her maiden major success to draw level at one-set apiece.
With the momentum going her way, Raducanu roared to 5-0 in the deciding set, winning 77 per cent of her first serve points to close out the victory.
Raducanu will next take on home favourite Ana Bogdan.
No.1 seed Simona Halep - who departed at the quarter-final stage of the Kremlin Cup last week - plays her first game on home turf on Wednesday against Elena-Gabriele Rusa and could meet Raducanu in the semi-finals.
Meanwhile, Romania's Jaqueline Cristian booked a second round clash with Australia's Ajla Tomljanovic after a marathon 3-6 7-6 (10-8) 7-6 (7-3) win over Slovenia's Kaja Juvan.
Sixth seed Marta Kostyuk of Ukraine cruised past American Bernarda Pera 6-3 6-4 to secure her last 16 berth.
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