At Edgbaston, Austin looked on course for her second century in three innings for the Bears before she offered a return catch to Jess Woolston six runs short.
But Em Arlott’s 44 from just 19 balls and Brooke Halliday, with 37, made sure the momentum was never badly lost as the home side reached 269-9, with Claudie Cooper (4-55) the pick of the Yorkshire attack.
Rain in Birmingham saw the visitors’ target brought down to 260 in 46 overs but Arlott returned to wreak early havoc with the ball, ending up with 3-24, with Phoebe Brett (3-59) backing her up to make sure Yorkshire’s threat was snuffed out despite a gallant 52 from Sterre Kalis.
The win moved Warwickshire up to third in the table and firmly in contention for a top-three finish with four games to go.
At Chelmsford, bottom club Essex were soundly beaten by Somerset as openers Odgers and Luff crashed centuries in a marvellous stand of 223 for the first wicket.
Odgers’ 133 came off 124 balls and Luff’s effort of 103 was compiled off 96 as the pair broke the back of their chase of 267 on their own.
That took the limelight away from the way Essex recovered from 15-2 to reach 184 thanks to a gutsy stand of 169 between Jodi Grewcock (87) and Sophia Smale, who went on to make a career-best 83.
Liberty Heap’s 39 took Essex beyond 250 before she was removed by Ellie Anderson (3-44), but the brilliance of Odgers and Luff made sure that was never enough.
