Carlos Tevez scored a penalty and set up two goals for Giovanni Moreno as Shanghai Shenhua made a blistering start to their Chinese Super League campaign with a 4-0 thrashing of last season's runners-up Jiangsu Suning.
Tevez struck nine minutes before half-time after Moreno had given Shenhua the lead and Mao Jianqing made it 3-0 in the 79th minute.
Tevez and Moreno combined again four minutes from time, while Alex Teixeira's sending off in injury time compounded the misery for Jiangsu.
"Today we have proved ourselves by defeating a great team such as Jiangsu," Poyet said. "I hope our fans can enjoy the win.
"I am extremely happy for Tevez. Goals are important, and he has started his CSL journey with goals."
The result means Shenhua are joint top of the early standings with city rivals Shanghai SIPG, who won 5-1 against Changchun Yatai on Saturday.
Defending champions Guangzhou Evergrande also started by collecting all three points against Beijing Guoan.
Brazil international midfielder Paulinho scored from close range three minutes before the end to secure a 2-1 win for Luiz Felipe Scolari's Guangzhou.
The former Tottenham Hotspur man had seen his 19th-minute opener cancelled out by Burak Yilmaz's 38th-minute penalty.
Zhao Hejing was sent off in the 66th minute for Beijing, only for the numbers to be levelled nine minutes from time when Guangzhou captain Zheng Zhi was dismissed.
"I hope we can keep winning," Scolari said. "Beijing have always been a good team and today they were well prepared.
"I'm very glad we won and I hope we can improve our possession in the next game."
Manuel Pellegrini's Hebei China Fortune made a disappointing start as they were held 0-0 by Henan Jianye, while Chongqing Lifan and Yanbian Funde also played out a scoreless draw.