In a downhill charge for the finish line in Katowice, where riders reached speeds of nearly 80kmh, the FDJ rider pipped Argentinian Lucas Sebastian Haedo by less than a half a wheel to win the third stage.
Australia's Allan Davis was third, retaining the overall lead ahead of stage two winner Andre Greipel of Germany by a mere three seconds.
Tuesday's sprint was so close that Haedo raised his arm in victory but Hutarovich said he knew he had the first ProTour win of his career safely in his saddlebag.
"When you're a sprinter you always know if you're first across the line, even if it's by two centimetres," Hutarovich said.
"It was a really, really fast sprint, I think I hit 77kmh at one point. But it's the chaotic, dangerous ones like today's where I seem to do the best."
"Whatever, it's a huge win for me, one of the biggest of my career, although taking Belarus's national road-race title twice was equally important."
Race leader Davis said the downhill dash for the line was "one of the fastest I've ever done. Sprinting on such a steep descent made it really hectic and crazy.
"In fact it was so fast you couldn't follow anybody's wheel in the last kilometre. When I crossed the line I thought I was second, but I couldn't be sure.
"Still, I've had three top three places in three days and the leader's jersey so I can't complain."
The shortest stage of the Tour was preceded by a minute's silence in honour of Italy team trainer and double Paris-Roubaix winner Franco Ballerini who died in a car accident in February.
Olympic and double world champion Paolo Bettini, who took over as national team coach after Ballerini's death, flew in specially to be present at the ceremony.
Third stage results: Sosnowiec to Katowice (122.1km)
1. Yauheni Hutarovich (Belarus / FDJ) 2 hrs 45 mins 04 secs
2. Juan Jose Haedo (Argentina / Saxo Bank) same time
3. Allan Davis (Australia / Astana)
4. Tom Veelers (Netherlands / Skil - Shimano)
5. Kenny Dehaes (Belgium / Omega Pharma - Lotto)
6. Wouter Weylandt (Belgium / Quick-Step)
7. Borut Bozic (Slovenia / Vacansoleil)
8. Robert Foerster (Germany / Milram)
9. Graeme Brown (Australia / Rabobank)
10. Alexander Kristoff (Norway / BMC Racing)
1. Allan Davis (Australia / Astana) 12 hrs 53 mins 14 secs
2. Yauheni Hutarovich (Belarus / FDJ) +4"
3. Aitor Galdos (Spain / Euskaltel) +8"
4. Juan Jose Haedo (Argentina / Saxo Bank)
5. Wouter Weylandt (Belgium / Quick-Step) +10"
6. Kenny Dehaes (Belgium / Omega Pharma - Lotto) +11"
7. Alexander Kristoff (Norway / BMC Racing) +14"
8. Chris Sutton (Australia / Team Sky)
9. Roy Sentjens (Belgium / Milram)