Zielinski's total weight of 385 kilograms equaled the result of Russia's Apti Aukhadov, but the Pole won the gold by virtue of lower bodyweight. World champion Kianoush Rostami of Iran got the bronze.
Poland had not won an Olympic gold medal in weightlifting since Zygmunt Smalcerz's flyweight triumph in 1972.
Dozens of Polish fans in the ExCeL centre chimed in as Zielinski bellowed out the national anthem at the medal ceremony.
But they were soon overtaken by an even louder contingent of Iranian fans waving flans and shouting "Iran" long after the medallists had left the stage.
Defending Olympic champion Lu Yong of China finished first in the snatch portion but bombed out with three failed attempts in the clean and jerk. World record holder and 2008 silver medallist Andrei Rybakou was among the four lifters who were eliminated already in the snatch.
The snatch is performed in one continuous move while the clean and jerk is a two-part lift where the bar is first raised to shoulder level before being pushed overhead.
Earlier Friday, Svetlana Podobedova took out revenge on her former homeland, Russia, by winning the women's 75-kilogram gold medal for Kazakhstan in a showdown with former Russian team mate Natalya Zabolotnaya.
Podobedova had a falling out with the Russian weightlifting federation after a two-year doping suspension in 2006. She switched citzenship to Kazakhstan, but Russia blocked her from competing in the Beijing Olympics.
In London, neither the Russian federation nor its two best lifters in the weight class could stop Podobedova as she clinched Kazkahstan's third weightlifting gold in London.
Zabolotnaya achieved the same total of 291 kilograms but finished second because of a higher body weight, while countrywoman Nadezda Evstyukhina, the 2011 world champion, surprisingly crashed out with three failed attempts in the snatch.
Her right hand on her heart, Podobedova cried as the Kazakh flag was raised in the arena.
"In 2008, Russia didn't allow me to go to Beijing but Kazhakstan gave me a chance," she told reporters afterward. "I started training for this slowly, and this gold is for Kazhakstan."
Zabolotnaya was on top after snatching an Olympic record 131 kilograms, 1 kilo more than Podobedova. But the Kazakh fought back in the clean and jerk, where the two rivals exchanged the lead lift by lift, breaking the Olympic record four times in the process.
The crowd roared as Podobedova cleared 161 kilograms in her final attempt to win the gold. Her coach broke into a spontaneous victory dance after what was the most exhilarating duel so far in the Olympic weightlifting competition.
Iryna Kulesha of Belarus was a distant third with 269 kilograms.
Egypt's Khalil Mahmoud Abir Abdelrahman was injured in her last lift when she fell backward from a squat and the bar struck her chest. She was taken off the platform in a wheelchair.
Asian lifters had won all weight categories before Friday. China now has four gold medals, while Kazakhstan and North Korea have three each.
AP Sports Writer Luke Meredith contributed to this report.