Coldplay, Haim and Kano were among the acts on the bill for Live At Worthy Farm, which had been due to start at 7pm UK time on Saturday but was delayed for around two hours.
Some ticketholders reported on social media they were unable to access the stream due to an "invalid codes" error message.
Following the delay, the show's co-promoters and producers, Driift Live, announced they were providing a free link.
They later tweeted to say they were offering those affected on the BST time zone extended access to the stream on Sunday.
They also said they would be offering a refund for those who required one, with tickets costing £20.
Their statement added: "All other ticket purchasers for the other timed streams remain unaffected. We send our sincere apologies to all those who were affected by tonight's technical
issues, but we hope they will all be able to enjoy this incredible show over the coming days."
Glastonbury festival organiser Emily Eavis also apologised for the technical issues.
She tweeted: "I am so sorry about the problems with the stream tonight. If you weren't able to get on, I'm told that the new link (http://Ink.to/ liveatworthyfarm) is working.
"We will obviously make sure we show the whole film again from tomorrow too and give you the chance to catch up on any bits you missed. I really hope you can enjoy the rest of it tonight. And, again, I'm just so sorry to anyone who's had issues."
Coldplay delivered an energetic performance from in front of the Pyramid Stage which included hits like The Scientist, Viva La Vida and Clocks.
The band started with their new song Higher Power, which they recently opened the Brit Awards with, performing from a pontoon on the River Thames.
As Martin launched into The Scientist, he said: "Wherever you're watching from, we send you our love and we wish you were here."
The singer also referenced the weather, which in true Glastonbury fashion saw rain come down as they performed, with Martin saying: "This is very weird but very fun, and we brought our own special rain effects, (it) looks completely genuine and I just want to make you all feel better if you're watching that.
"If there's a day you didn't want to stand in a field it's probably today but ... we're happy to be here, so happy. We want to thank the Eavises and everyone that has got this together because it's been a big deal and it's the first time we've played to thousands and thousands of cows so I hope we're doing OK."
Introducing their song Fix You, he said it was "for all the doctors and nurses, everyone who worked so hard".
Also on the bill, Damon Albarn paid tribute to Afrobeat drummer Tony Allen, following his death aged 79 last year.
Before performing The Good, The Bad and The Queen's The Poison Tree, Albarn said the song was "somehow fitting for him as a memory and really for everybody's Tony because everybody's felt some kind of loss during this period, so this is for everybody's Tony".
Radiohead's Thom Yorke and Jonny Greenwood debuted music from their new project, The Smile, which also includes drummer Tom Skinner (who plays in Sons of Kemet), as well as Radiohead producer Nigel Godrich.
The Smile is named after the Ted Hughes poem of the same name.
Mercury Prize-winning band Wolf Alice were the first to perform at the event, which had seen people pay £20 for a ticket prior to the stream being made available for free.
Festival founder Michael Eavis delivered a spoken-word narration before Wolf Alice's performance, which was followed by a spoken word performance from poet Kae Tempest.
Last year's Mercury Prize winner Michael Kiwanuka performed songs Hero and Cold Little Heart during his set, while George Ezra opened his set with his popular song Blame It On Me.
British musician Kano received plaudits on social media for his impactful performance, with one viewer tweeting: "Alright @glastonbury you redeemed yourself."
Another tweeted: "We might have missed half the acts but Kano is killing this!! Highlight of the night! @glastonbury @TheRealKano".
The event also included performances from Jorja Smith and DJ Honey Dijon ft Roisin Murphy, as well as a poem reading from George The Poet.
Saturday night's show will support Oxfam, Greenpeace and WaterAid, the festival's three main charity partners, after the full festival was cancelled for a second consecutive year due to the coronavirus pandemic.