Bears went into their game against Hampshire at the Utilita Bowl in second place, one point ahead of the Blaze and seven clear of Lancashire in fourth.
They were in trouble on 40-4 and later 92-7 as spinner Bex Tyson picked up 3-27 for the Hawks.
But Perrin kept her nerve, reaching 50 off 34 balls with a lofted drive and put on 52 with Georgia Davis (15) before she sliced a full toss from Perry (2-23) to mid-off and was caught.
Perry opened the batting for the hosts and reached her first Blast 50 from 36 balls in an opening stand of 75 with Rhianna Southby (29). But they were unable to stay with the required rate and scoring 63 off the final five overs was beyond them, despite Georgia Adams’ unbeaten 32.
The Blaze were not at their best with the bat after winning the toss against Essex, with sisters Sarah and Kathryn Bryce both falling to Abtaha Maqsood in the same over as they struggled to 51-4.
Heather Graham top scored with 33 and Sarah Glenn (17) and Lucy Higham (14) added 30 valuable runs before Eva Gray (4-18) took three wickets in four balls in the final over as they were all out for 139.
Essex lost Lauren Winfield-Hill, caught off Glenn for eight, and fell behind the asking rate despite 33 off 31 balls by Jodi Grewcock. It was Grewcock’s dismissal by Glenn (3-17) that triggered a collapse from 77-3 to 86-9 in which the home batters merely provided catching practice.
Kate Coppack and Maqsood prevented them being bowled out but they finished well short.
“We’ve tried not to think about Finals Day, obviously we’re super pleased but we’ve got two tough games on the road to come and it’s about trying to build momentum and put pressure on Surrey because we still want top spot,” Bears skipper Gordon said afterwards.
