Applegate qualified fastest for the final, winning heat one in 2:14.31.
23-year-old Massey was also impressive, coming second in heat three with a time of 2:16.21.
It was bad news for fellow Briton Chloe Davies though, who just missed out on a place in the final.
Davies swam 2:18.10 to finish third in heat two. She will now be first reserve should someone pull out of the final.
The final takes place at 5.56pm this evening.