Parker's 78th-minute thunderbolt settled a roller-coaster clash at Upton Park on Saturday and West Ham's 3-2 victory pushed them to the brink of Premier League survival.
The Hammers' superior goal difference means Hull cannot realistically overtake them, while Burnley went to Anfield on Sunday knowing anything but a victory would see them suffer the same fate.
West Ham fell behind after just three minutes through a Jonathan Spector own goal but hit back to lead at the interval with strikes from Ilan and Radoslav Kovac.
After Hugo Rodallega equalised for Wigan, the game appeared to be heading for a draw until Parker slammed home the decisive goal from 25 yards.
Zola's ambitions at the start of the campaign were greater than simply survival but given the turbulence that has hit the club this season, it would stand as an achievement he can be proud of.
"Staying up would be a big big deal because we've had to deal with so many problems this season. You only know half of them," said Zola.
"It's been difficult, but despite that we've stuck together and produced a good result and this will change our season. Players have put a lot into this season, not just physically but mentally.
"It's been an emotional year and Scott's goal was an unbelievable moment. The game was going flat and the goal was unexpected.
"I understand there was a lot of pressure on myself, the players and the crowd so it was a big relief."
West Ham's perilous financial state meant that key players like James Collins had to be sold to raise cash and the club would have gone into administration with debts of £105million had David Gold and David Sullivan not taken charge.
Speculation is rife that Gold and Sullivan are looking to replace Zola in the summer, with the likes of Mark Hughes and Steve McLaren linked with the job.
West Ham insist no decision will made about the manager until the end of the season.
Zola believes this campaign has given him five years' worth of experience.
"I am not thinking about trying to make a point. But what doesn't kill you makes you stronger and everyone will be stronger for this experience," he said.
"The future is important but I'm not going to spend time right now speaking about things because I don't know how things will turn out."
Parker not only scored the winning goal on Saturday but he produced another Herculean performance.
Alongside Mark Noble, Parker provided an inspirational midfield blend of drive, dynamism, courage and creativity. There was no competition for the man-of-the-match award.
Parker threw himself into tackles with little concern for his own wellbeing but also launched the counter-attack that led to Ilan's goal and sealed three vital points.
"For me he is the complete midfielder and I rate him as one of the best in this country," said Zola.
"He is very good at recovering the ball and using it. He can tackle and transform a defensive action into an offensive one with his running with the ball and ability to see a pass.
"He's been doing it week in week out for us. The problem is that right now England are very strong in midfield.
"But I'm sure Fabio Capello is keeping an eye on him and I would be delighted if he made the World Cup."
Wigan manager Roberto Martinez expects to field bids for some of his star names this summer - but he insisted Wigan are under no pressure to sell.
"We are fighting to avoid the drop and you have so many teams talking about our players - Charles N'Zogbia, James McCarthy, Victor Moses, Hugo Rodallega. That shows that we are doing something well as a team," said Martinez.
"That should be a strength not a negative. I want the top sides in Europe to talk about Wigan's players.
"We need to stop worrying about losing players. If Manchester United can't hold onto Ronaldo then, with respect, I don't think we have a chance of holding players who want to move on.
"Financially we are in a good position and we don't need to sell players on the cheap. We are not forced to balance the books and that is a strong position in football.
"The fans know that and understand that if we have to sell it is for the right reasons and that Wigan will be a stronger club.
"If we stay up it will be a huge achievement. We will need to be a little creative in our recruitment in the summer."