The Bray-born boxer sunk to her knees as she was given a 10-8 points verdict after four close rounds.
26-year-old Taylor, for so long the star of the division, had been expected to bring her best to London in front of a passionate Irish crowd at the ExCeL Arena.
But Ochigava, who had cast doubt over the impartiality of the judges in the lead-up to the fight, was in determined mood and a cagey opening round was shared 2-2.
The Russian's spoiling tactics made it difficult for Taylor to score, and a couple of trademark left hooks from Ochigava gave her a slender 4-3 lead at the halfway point.
That only inspired the crowd to sing louder still for their heroine, and a couple of hooks of her own in the third round began to turn the tide in the contest, giving her a two-point advantage to carry into the final round.
Taylor had to remain calm to preserve that gap in the last two minutes, staying out of trouble as Ochigava looked desperately to claw the deficit back.
But she hung on in a last round that was tied and looked visibly nervous as she awaited the decision before going to her corner to hug her coach and father Peter and running around the ring with an Irish flag.
"It's a dream come true," Taylor told a news conference also attended Peter who said it was his daughter's destiny to be Olympic champion.
"I've envisaged this moment so many times. I've no intention to stop, I have 10 years in me. Pro or amateur, not sure yet. I will make a decision in the next few weeks."
Exiting the arena close to tears, she hugged former world professional Irish champion Barry McGuigan who told a ringside reporter that it was 20 years to the day since Ireland won its last boxing gold, Michael Carruth's in Barcelona.
Ochigava departed far from happy with the outcome.
"As usual they tried their best to let the Irish win, the judges as usual corrected the scores in her favour just as they did during the world championships to let Katie win," Ochigava told reporters through a translator. "What can I say now."
Ireland, who also have three fighters left in the men's semi-finals, last won an Olympic gold when Michelle Smith swam to three victories in 1996, but those were tarnished by her suspension in a doping controversy two years later.
That long wait saw fans draped in the green, white and gold of the Irish flag fill the Excel centre with chants of "Ole, Ole, Ole", a chorus usually reserved for Irish soccer matches, as well as Irish sporting anthem "The Fields of Athenry".
Their cheers were joined by congratulations from home.
"Katie Taylor is not only an Olympic champion, she is a force of nature whose pioneering spirit and boxing brilliance have seen her realise her personal dream of winning Olympic gold," Irish prime minister Enda Kenny said in a statement.
"She has won the hearts and minds of the Irish people who admire her greatly and love her to bits."
In Taylor's home town of Bray, just outside Dublin, an estimated 10,000 people watched the fight on two big screens on a soccer pitch, a stone's throw from the new Olympic champion's home and where she went to school.
As the commentator said "and the gold medal is on its way to Bray" just seconds before last bell went, the crowd went crazy. Flags were being waved and huge jets pumped confetti into the air when she was announced the winner.
Losing semi-finalists Mavzuna Chorieva of Tajikistan and Brazilian Adriana Araujo took bronze.