Worcestershire Rapids captain, Moeen, Ali and 2022 overseas signing Matthew Wade have already made their mark at the 2021 ICC T20 World Cup.
The duo helped England and Australia make a winning start to their campaigns against the West Indies and South Africa, respectively.
Moeen played a vital role with the ball as the holders West Indies were bowled out for 55 in Dubai.
He took the new ball, bowled his four overs straight through, and finished with excellent figures of 4-1-17-2.
Moeen had opener Lendl Simmons caught at deep mid-wicket by Liam Livingstone in his second over and in the next – a maiden – Shimron Hetymer holed out to England captain Eoin Morgan at mid-on.
He delivered 18 dot balls and also held onto a catch to dismiss the other opener, Evin Lewis, off Chris Woakes.
Jos Buttler’s unbeaten 24 saw England to victory in 8.2 overs.
Wade kept wicket for Australia and held onto two catches as South Africa were restricted to 118-9 in Abu Dhabi.
Australia were also struggling for runs, and the game was in the balance when Wade came to the wicket at 81-5 in the 16th over.
But he showed all his experience in making 19 not out from just ten balls and collected two boundaries off Kagiso Rabada as he and Marcus Stoinis (24 not out) saw Australia home with two balls to spare.
Moeen and England are next in action against Bangladesh in Abu Dhabi on Wednesday, while Wade and Australia face Sri Lanka in Dubai on Thursday.