Their track Cold Heart (Pnau Remix) claimed the top spot after spending three consecutive weeks at number two in the Official Charts Company rankings.
It has recorded 64,000 chart sales and 5.9 million streams.
It is the first time Sir Elton has had a number one single since he appeared on rapper 2Pac’s posthumous 2005 single Ghetto Gospel.
Sir Elton and Lipa’s success brings to an end Ed Sheeran’s four-week reign at the top of the chart with Shivers, which has dropped to second place.
Earlier this week Sheeran had urged his fans to help Sir Elton beat him to number one.
Love Nwantiti by CKay is at number three, with Boyz by Jesy Nelson featuring Nicki Minaj at four.
Glass Animals track Heat Waves is in fifth place.
In the album chart Sam Fender earned his second number one with Seventeen Going Under.
His album amassed 44,000 chart sales, meaning it had the fifth biggest opening week of 2021.
Drake’s Certified Lover Boy ranked second, followed by Olivia Rodrigo album Sour.
James Blake album Friends That Break Your Heart debuted at number four, followed by Doja Cat’s Planet Her in fifth.