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Goulding congratulated the happy couple: "Congratulations Harvey and Hayley, you're both heroes and we all love you."
The couple thanked her for joining in on the celebrations and clapped for her after the performance.
The pop star performed at Prince William and Kate Middleton's wedding in 2011. She had previously sung Love Like You Do at the One World: Together At Home concert held over the weekend.
According to a post by For Better For Worse on a fundraising website, the wedding directory company organised the wedding after hearing the couple's story.
"We heard of a lovely couple named Hayley and Harvey that were meant to be married on Saturday 11th April," the post read.
"They have unfortunately had to postpone their special day until October because of recent events.
"In light of Hayley and her family's dedication to the NHS and the hard work of all the key workers on the frontline, we have decided to create a fundraising campaign for NHS Charities Together, a collection of more than 250 not-for-profit organisations around the UK that help our hospitals do more."
• Covid19.govt.nz: The Government's official Covid-19 advisory website
The heartwarming moment Goulding joined in on the nuptials was posted on the company's YouTube channel.