Vikas clinched the contest 9-8 with a calculated performance to set up a clash with Ukraine's European Championship bronze-medallist Taras Shelestyuk, who stunned third seed Andrey Zamkovy of Russia on countback after both the boxers ended the regulation three rounds at 13-13.
Earlier, L Devendro Singh (49kg), Manoj Kumar (64kg) and Jai Bhagwan (60kg) lost their respective quarterfinal bouts to bow out of the mega-event.
The 19-year-old Vikas, competing in the last bout of the day in his maiden World Championships, started aggressively, attacking his rival with jabs and right hooks in the opening round itself. But at the end of the round, the two boxers were locked 2-2.
The Indian, who had won gold in 60kg category in the Asian Games, was a tad more guarded in the second round and the calculated approach paid off as the ocassional punches he connected put him a point ahead of his rival at 5-4 overall.
In the final round, both the boxers were aggressive but Vikas was more precise in his timing of punches which ultimately proved the clincher.
"It is all god's grace and my parents' blessings that I have managed to come this far," an emotional Vikas told PTI from Baku.
"I was very aggressive in the first round and thought I was up at the end of it but when the coaches told me that the score is level, I decided to be slightly defensive. Instead of attacking too much, I focussed on timing my punches and the strategy paid off," he said.
The teenager, who gets a day's break before stepping into the ring on Friday for the semi-finals, said he was not at all intimidated by the prospect of facing a fancied rival.
"I have my preparations in place and the rest is in god's hands. When I came here, I was banking on my focus, preparation and god's blessings for doing well. It has been so far so good and hopefully it would continue," he said.
If Vikas manages to win on Friday, it would be an improvement on the bronze medal that Olympian Vijender Singh (75kg) managed in the previous edition. Vijender was ousted in the first round in this edition.
Earlier, assured of Olympic berths after reaching the quarterfinals, the losing Indian trio was aiming for medals at the mega-event but it was not to be as Devendro lost to Asian champion and second seed Shin Jong Hoon 16-28 while Manoj went down to fifth seed Thomas Stalker of England 18-24. Jai was beaten 10-11 by Kazakhstan's Gani Zhailauov.
The 19-year-old Devendro, who has proved to be a pint-sized dynamo in his maiden senior international tournament, finally found a match in Hoon after an impressive giant-killing spree.
The Manipuri was his usual spunky and energetic self as he opened the day for India but Hoon got a measure of his game quite early on in the bout.
The 23-year-old Korean, who was a bronze-medallist at the previous World Championships, withstood the initial onslaught from his eager rival before launching his attack.
Taller and more experienced, Hoon kept a shell guard and invited Devendro before attacking him with some telling jabs. He ducked craftily and took advantage of his better reach to catch Devendro off guard on several occasions to be up 11-9 in the opening round.
The second round followed a similar script as Devendro managed just five points against his rival's nine to be down 14-20 overall.
The frustration showed when the Indian hit his rival thrice after the bell had gone in the second round. The third round was an all-out slug fest with Hoon managing to connect more often to wrap up a rather comfortable win.
Next up was Commonwealth Games gold-medallist Manoj. The 25-year-old was up against another CWG gold medallist (in the light weight 60kg division), who went on to clinch a silver at this year's European Championships.
Both the boxers treaded cautiously initially and it was Stalker who opened up first by lowering his guard.
With a left hook that fetched him points whenever he wanted, Stalker seemed in control from the very start even though the opening round scoreline had the Indian trailing by just a point at 4-5.
Manoj tried hard to break his rival's rock-solid defence with uppercuts but Stalker, at an imposing 5'10, didn't seem too affected. Using left hooks and jabs, Stalker built on his lead to make 16-11 after the second round.
Manoj fought hard in the final round but the effort could not wipe off the lead he had conceded as the 27-year-old Englishman clinched the issue.
The evening session also started on a disappointing note for India as Jai Bhagwan lost 10-11 to Zhailouv in what seemed more of a wrestling bout with both the boxers holding and clinching each other constantly.
The opening was 3-3 with hardly anything separating the duo. In the second round, the Kazakh boxer got the decisive one-point lead to make it 6-5 in the overall scoreline.
In the third round, both the boxers tried hitting each other from a distance but invariably ended up in clinches and were lucky not to be warned for the tactics by the referee.
Vikas shines; 3 others lose in World Championships
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