Huw Jones went over for two tries and showed up well at centre alongside his Glasgow and Scotland partner Sione Tuipulotu.
Scott Cummings was a standout performer in the pack after being promoted from the bench following the late withdrawal of Henry Pollock.
However, there were too many periods where the Lions appearded disjointed and frantic with a big error count.
Jones went over for two first half tries with Fin Smith converting each time to put the Lions into a 14-0 lead.
The Waratahs responded through wing Darby Lancaster just before half-time and hooker Ethan Dobbins powered over just after the interval to make it a four-point game.
Scrum-half Alex Mitchell dummied his way over for the tourists' third try on the hour mark with Smith adding the extras but the Lions could not build on their lead and had to be content with the 21-10 win.