The hitmaker could be heard fighting tears as she launched into a performance of the chart smash Lonely Together, which was released in 2017 and performed on Strictly Come Dancing.
Before singing, she said: “It’s gonna be hard for me to sing this song.
“I had the honour of collaborating with somebody who changed my life, and he was a very good friend of mine.
“I haven’t sang this song that we did together since he passed away.”
She added: “We collaborated for the last song that he released.”
The 27-year-old then led a minute’s silence before starting to sing; her voice audibly quivering in the first verse.
Last week it was reported that Avicii died of an apparent suicide, after his family posted a touching statement.
“He really struggled with thoughts about meaning, life, happiness. He could not go on any longer. He wanted to find peace,” they said.
“Our beloved Tim was a seeker, a fragile artistic soul searching for answers to existential questions.
“An over-achieving perfectionist who traveled and worked hard at a pace that led to extreme stress.”
The Swedish DJ and producer was only 28 at his time of death on April 20 – and several of his works have since returned to the charts.
Wake Me Up, a former Number One, returned to the Top 40 at Number 26, while Levels returned to Number 36.
His album True leapt up to Number 14 on the album chart, while Stories hit Number 17.
Lonely Together peaked at Number 4 in this country, and was also a Top 3 smash in his native Sweden.
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