The African champions were reeling after being held to a surprise 1-1 draw at home to Sierra Leone before slumping to a stunning 1-0 defeat at tiny Niger in their first two Group G games of the qualifiers.
Shehata came in for widespread criticism but Egypt signaled their intent to make amends with a convincing display against Australia in Wednesday's friendly at Cairo Stadium.
ENPPI striker Ahmed Abdul-Zaher opened the scoring in the 29th minute for his first international goal and Geddo, Egypt's hero during their triumphant Nations Cup campaign last January, doubled the lead on the hour mark.
Borussia Dortmund striker Mohamed Zidan, making his long-awaited comeback after a seven-month injury layoff, wrapped up the victory in stoppage time after converting a penalty.
"We regained some of our lost confidence after tonight's win," highly-successful coach Hassan Shehata told reporters after the match.
"We faced a tough opponent in Australia who played at the World Cup more than once, it wasn't an easy game.
"The victory benefited us and boosted our morale after the poor results during the past period. I hope the fans and media will be patient and wait for further improvements."
Shehata introduced several new faces in the starting line-up due to the absence of some key players including skipper Ahmed Hassan and strikers Emad Meteb and Amr Zaki.
Holding midfielder Ibrahim Salah, central defender Ahmed Duiedar and striker Abdul-Zaher caught attention with a lively and energetic display to give Shehata extra options.
"They made a strong start to their Egypt career," Shehata, under whom the Pharaohs won three consecutive Nations Cup titles, added.
"The confidence of the new players was also affected by the past results but they were very good today."