Patel, the Bears captain and talismanic overseas off-spinner, put the skids under Yorkshire, who raced to 80 without loss in the 13th over. They finished with 247 for nine.
He took all of his wickets as the Vikings slipped to 149 for six in the 30th over, with India batsman Che Pujara’s 96-ball 73 standing out after the hosts elected to bat.
Left-handed opener Ed Pollock then hit Tim Bresnan for a straight six in the first over as his dashing 26 got the chase off to a positive start.
Hain, who faced 110 balls, shared 87 inside 19 overs for the second wicket with Jonathan Trott (50) and 97 inside 14 with Adam Hose for the fourth.
He went on to complete his second successive century to help Warwickshire bounce back from Thursday’s opening day defeat at home to Derbyshire, winning by five wickets with 4.2 overs remaining.
Yorkshire, who have also won one and lost one in the North Group, will be frustrated they were unable to build on the opening stand between Tom Kohler-Cadmore (39) and Adam Lyth (38).
After Aaron Thomason’s bustling seamers made the breakthrough by getting Kohler-Cadmore caught at deep gully, Patel trapped Lyth lbw two balls later.
The New Zealander then had Jack Leaning and Adil Rashid caught behind and bowled Andrew Hodd, with his three wickets coming in as many overs as the score fell to 149 for six in the 30th.
Olly Stone backed Patel up with two wickets, while wicketkeeper Tim Ambrose claimed five catches in a sharp Warwickshire fielding display.
Pollock’s four fours and a six in his 21 balls then allowed the visitors to get ahead of the rate, with his opening partner Trott and Hain calmly advancing to the target.
They took the score beyond 100 in the 19th over and matched each other run for run through the forties.
But Trott was run out coming back for two to deep cover as the score fell to 126-2 in the 25th. His first run brought up 50.
Ian Bell then followed caught at slip in the next over, bowled by left-arm seamer James Wainman, but Hain and Hose ensured Yorkshire hopes were only briefly raised.
Hose dominated their partnership and hit 44 before handing Ben Coad a consolatory wicket. Wainman also picked up his second wicket before Hain reached his hundred off 107 balls, including 12 fours.
Next Home Game: vs Northants - 30 May
Warwickshire return to Edgbaston on Wednesday 30 May at 11am when they host Northants. The visitors have a strong bowling attack and bolstered this year by Brett Hutton joining the club and he will a welcome addition to their Royal London One-Day Cup side, the competition where Northants failed to compete for the knockout stage last year hampered by a bad run of injuries. But a quarter-final appearance in 2016 suggests a run at qualification is possible and they will certainly provide tough opposition for the Bears.Buy tickets