Zimbabwean McGregor, who was working for Scotland's Alastair Forsyth, suffered a heart attack on the ninth hole at Santo da Serra, a steeply undulating course more than 2,000 feet above sea level.
An indefinite suspension of play was initially announced, but the decision was later taken to resume play at 6pm, with England's Daniel Brooks eventually beating Scotland's Scott Henry on the first play-off hole.
Brooks admitted that the tragedy had cast a shadow over his maiden European Tour title success.
"It's great to get a win, but it's not nice to do it in these circumstances. It's horrible what happened out there so my condolences go out to all of his family," he said.
Henry added: "I'm obviously disappointed to be beaten in a play-off but after the week and everything that's happened, it puts things into perspective."
While the winner and runner-up neglected to criticise organisers for letting play continue, the decision to finish the event was criticised by a number of their peers, including Sweden's Joel Sjoholm who had previously worked with McGregor.
"Can't believe that they are sending out players to finish the 2nd and final round when someone just died on the course!!!," Sjoholm, who missed the 18-hole cut in Madeira, wrote on Twitter. "R.I.P my dear Mac! Way too young! This going to be a tough evening!"
France's Jean-Baptiste Gonnet, who also missed the cut, added: "Can't believe there are still playing in Madeira. there is no respect anymore. how you can even walk on the 9th fairway. RIPmac."
Spain's Gonzalo Fernandez-Castano wrote: "Really sad news from Madeira. We are going to miss you Mac. One of the nicest guys on Tour. £RIPIainMcgregor."
Forsyth, however, explained that he had a part to play in the decision.
"Myself and playing partners Adam [Gee] and Tano [Goya] met tournament officials and spoke to George O'Grady [European Tour chief executive] on the phone before taking the decision to play on, because we felt that was what Mac would have wanted," said Forsyth.
A statement from the European Tour read: "It is with great sadness and deep regret that we report the untimely passing of caddie Iain McGregor during play on the final day of the Madeira Islands Open - Portugal - BPI.
"Everyone at The European Tour extends our deepest sympathies to the friends and family of Iain at this time.
"Following consultation with the players and caddies involved, however, it has been decided that play should continue and the tournament should finish.
"A minute's silence has taken place at the clubhouse and play resumed at 6.00pm local time. "
Nine-time major winner Gary Player led the tributes on Twitter, writing: "RIP Big Mac. You will be missed. My condolences."
And McGregor's fellow Zimbabwean Tony Johnstone added: "Just heard very sad news of passing of my friend Ian MacGregor (Zim Mac) whilst caddying in Madeira. A top man and will miss him. RIP Mac."