Leicester Tigers full-back Freddie Steward sliced through for England’s opener on six minutes but James O’Connor’s boot kept a dogged Australia in the contest, making 16-15 at half-time.
England advanced on the scoreboard via penalties and replacement hooker Jamie Blamire, of Newcastle Falcons, scored in the final play of the match to seal the win.
Bath Rugby flanker Underhill started the game and was instrumental throughout. Usually talked about for his defensive quality and breakdown destruction, the 25-year-old was explosive with ball in hand and linked up nicely in some promising home attacks.
He carried the second most for an England forward, making 18 metres, one clean break and beating one defender.
Ewels and Stuart were introduced in final 10 minutes to help see out the win, earning their 25th and 14th caps respectively.