Mhairi Black defeated Labour's election campaign chief Douglas Alexander in Paisley and Renfrewshire South.
"This has clearly been a very difficult and disappointing night for the Labour party," Ed Miliband said after holding onto his own constituency seat.
An exit poll indicated that the SNP could win 58 out of 59 seats in Scotland, making it the third-largest party in parliament, behind the Labour Party.
According to the latest exit polls, Prime Minister David Cameron's Conservative Party is on track to win an overall majority.