Henriques top-scored with an unbeaten 49 off 23 balls as Sydney made an imposing 185 for five batting first and he then claimed three for 23 off three overs as Indian Premier League superpowers Chennai were limited to 171 for nine in reply.
Among Henriques' victims were India internationals Suresh Raina, who had threatened to take his side home before being dismissed for 57, and Mahendra Singh Dhoni (eight) in the same over as the Chennai run chase suffered a setback it could not recover from.
In what was the opening match in Group B, Sydney were given a flying start as Australia star Shane Watson continued his good form from the World Twenty20 - when he was named player of the tournament - by clubbing 46 off 30 deliveries before being run out.
Captain Brad Haddin kept the scoreboard ticking over but it was the fifth-wicket stand between Henriques and Steve Smith that powered Sydney to a total that ultimately proved just beyond Chennai.
Henriques did most of the damage, smashing three sixes and five fours, as the duo added 61 runs in the final four overs before Smith fell to the last ball of the innings for 26.
Chennai suffered a poor start to their reply when Murali Vijay was bowled for three by Mitchell Starc but Mike Hussey (16) - one of three Australians facing their countrymen - Faf du Plessis (43) and Raina got the Indian side back on track and at 141 for four in the 17th over, the outcome remained in the balance.
But man of the match Henriques' double breakthrough to get rid of Raina and the dangerous Dhoni proved crucial and Chennai, IPL winners in 2010 and 2011 and runners-up this year, fell short.
Starc took two more wickets in the final over to finish with three for 31 off his four overs.
In the day's other game an unbeaten century stand between Neil McKenzie and Quinton de Kock secured an entertaining eight-wicket win for Highveld Lions against defending champions Mumbai Indians in their Champions League T20 Group B match at the Wanderers.
Mumbai had set their opponents a target of 158 to win and that total looked beyond them in the early stages with runs hard to come by.
But McKenzie (68 not out) and De Kock (51no) both steered the Lions to victory with seven balls to spare.
The Lions had won the toss and elected to field, but some wayward bowling helped their opponents reach a competitive 157 for six in their allotted overs.
Opener Dwayne Smith scored a useful 26 off 19 deliveries before his dismissal lbw by Chris Morris, while Rohit Sharma (27) and Mitchell Johnson (30) - on his debut for the Indians - also chipped in to boost the IPL team's innings.
Sohail Tanvir took two wickets for the Lions, but the bowlers often struggled for rhythm and added 24 extras to Mumbai's total.
The Lions' reply began slowly and things looked to be going against them when they had reached just 37 for two after 6.5 overs.
However, McKenzie and De Kock first steadied the ship and then began to increase the knots as they smashed Mumbai's familiar bowling line-up - including the likes of Lasith Malinga, Harbhajan Singh and Pragyan Ojha - around the ground at will.
McKenzie was the first to reach his fifty off just 33 balls while De Kock passed the mark from 32 balls, shortly before hitting the winning run off Sri Lanka paceman Malinga to spark celebrations among the home crowd.
The pair added 121 runs between them, McKenzie smashing 68 off 41 deliveries, including 12 boundaries, and De Kock's 51 coming off 33 balls and featuring two sixes.
- Suresh Raina
- Mahendra Singh Dhoni