The undefeated Cup pairing accounted for Germany's Philipp Petzschner and Benjamin Becker 6-3 6-2 2-6 7-6 (7-4) at Rothenbaum Stadium to hand Australia a 2-1 lead.
Bernard Tomic takes on Florian Mayer at 11.30am (1930 AEST) in the opening match of Sunday's reverse singles with Petzschner expected to replace Cedrik-Marcel Stebe as Hewitt's opponent in the potentially decisive rubber.
Australia must win one of the two singles rubbers to return to the elite World Group for the first time since 2007, having lost playoff ties in four of the past five years and boycotted India in 2009 amid security concerns.
Despite holding the advantage, Australia will know promotion is anything but a fait accompli after blowing 2-1 leads with twin reverse singles defeats against Belgium in 2010 in Cairns and against Switzerland in Sydney last year.
World number 25 Mayer was in outstanding form on the opening day, blitzing Hewitt in straight sets.
"Bernie is a unique player," Hewitt said. "He could come out and worry Mayer a lot, so we will wait and see.
"I will be ready if I am needed."
The win was Hewitt's 50th in Davis Cup rubbers with a 38-12 record in singles and 12-3 in doubles.
The victory extended Guccione's Davis Cup doubles record to 7-0 and 4-0 in the competition with Hewitt.
The big red head was the only player not to drop serve in the two-hour, 31-minute contest with Hewitt more than playing his part with his boundless energy and court craft.
After being hammered by Mayer on Friday, Hewitt was highly animated even by his standards and produced his trademark aggression as Australia dominated the early exchanges.
He roared "Come on" as early as the fourth game as the Australians piled the pressure on Becker in the German's first Davis Cup doubles outing.
Becker's serve crumbled and the visitors had raced out to a two-set lead just after the hour mark.
With a demolition on the cards, the home team lifted and broke Hewitt's serve twice to force the match to a fourth set.
The Australians claimed an early break to stem the flow but at 4-3, the Germans peppered a Hewitt service game and eventually broke him on the seventh break point.
A tie-breaker was required and the Australians prevailed with Hewitt jumping into Guccione's arms after winning match point.
"The Germans were coming back at the boys and they showed really good fighting spirit," Davis Cup captain Pat Rafter said.
"We were very happy it did not go into a fifth set."
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