Hewitt, a former world No. 1 in the men's division, pasted Vladimir Voltchkov, 6-2, 6-1, 6-2.
"It was an awkward match to go out there and play," said Hewitt. "I knew I was heavily favored to go out there and win, but with Davis Cup, I've been in enough big ties and been the underdog in that many big matches that it's a different kind of pressure and it sort of levels itself out ... the competition out there."
Guccione needed five sets to overcome Max Mirnyi, 7-6 (7-4), 3-6, 7-5, 3-6, 6-4.
With its commanding 2-0 advantage, Australia can wrap the tie on Saturday when its doubles duo of Wayne Arthurs and Paul Hanley faces Mirnyi and Voltchkov.
Australia has 28 Davis Cup titles. Belarus has never won the event.