Held by the A-League outfit at Allianz Stadium, Spurs had been chasing a third win from three matches on their pre-season tour, having beaten Milton Keynes behind closed doors before opening their trip to Oceania with a 2-0 win over Auckland courtesy of goals from Richarlison and Dane Scarlett.
Mathys Tel was the standout performer once again, curling a stunning 25-yard free-kick into the top corner in the 29th minute to give Tottenham the lead, linking up well throughout with Rio Kyerematen, who was deployed at left-back ahead of summer signing Andy Robertson.
The Scot, who joined on a free transfer after leaving Liverpool, came on for his Spurs debut in the second half and looked a threat down the left with his crossing. Sydney levelled when a mistake from Kota Takai let Takahiro Sekine in to clip the ball over Martin Dúbravka, and the hosts almost snatched a winner as Robertson picked out young winger Yang Min-Hyeok, who spurned two clear chances.
The shootout swung Tottenham's way after Joe Lacey struck the post from 12 yards for Sydney and Jamie Donley, who has impressed De Zerbi this summer, saw his effort saved; Aleksandar Popovic then forced another good stop from Dúbravka before Scarlett stepped up to seal the win and a third victory in as many matches heading into Saturday's game against Chelsea.
Speaking afterwards, De Zerbi explained why several key players, including Micky van de Ven, Dominic Solanke and Jan Paul van Hecke, had again been left out.
"I thought today they were not yet ready to play without risk," he said. "Maybe some of them can play the next game Saturday with Chelsea, maybe not at the beginning. Maybe in the beginning Robertson and Sandro Tonali, but it's the management of the players, especially after World Cup or after big injuries like Udogie or Solanke.
"They suffered long injuries last season, and after a long trip, after the jet lag, after the beginning of the pre-season, I wouldn't like to take any risk."
On midfielder Mateus Fernandes, who also missed out, De Zerbi added: "Fernandes is just fatigued, the calf, and also for him we took the decision not to take any risk and to recover, but the next week, Wednesday, when we start the pre-season in London, he will be ready to work."
The manager also had praise for teenage forward Luca Williams-Barnett, who scored in the shootout: "He is a precious diamond. We have to work on him in the final third and he must work hard on his physicality. I've worked with a lot of young players in my time and he's a potentially special player."