Rob Burrow then touched down before Kevin Sinfield added a kick to make it 16-0 to the hosts.
St Helens began their comeback just before the half-hour mark when Louis McCarthy-Scarsbrook went over and Iosia Soliola added another try just five minutes later. Tom Makinson successfully kicked both conversions to make the score 16-12 at half time.
The visitors began the second half as they finished the first, with Makinson touching down just four minutes after the restart.
Anthony Laffranchi then capitalised on a Leeds error to put the Saints in front for the first time before Makinson grabbed his second try of the match to extend that lead to 10 points.