The first five games were all drawn, with Steere taking advantage of his 35 start to win the final match-up of the evening 7-5.
Craneswater A came from 0-4 down at home to Broadoak Social Club to triumph 8-4.
Graham Shervell and Lance Cornwell put Broadoak in control but Craneswater hit back to lead through Adrian Binding, Andy Boulton (45 break) and Mark Jones.
In the final game, Rob Kirby - who had a 45 start - made a 54 clearance on his way to a brace.
North End Bowls Club moved to the top of League A after a 7-5 victory over Cowplain Gas.
Bowls pair Richard Jones and Derek Sandy won their games with Cowplain Gas replying through the ever reliable Paul Lees.
Mark Richardson’s victory clinched a 7-5 win for Craneswater R at Bellair X.
Pete Parsons had earlier put the visitors ahead but that was cancelled out by Gary Linter.
The other Bellair highlight was Kenny Morgan making a 35 break in his drawn match.
Wins for Dave Pink and last man Gary Wilton helped Waterlooville C defeat League C table-toppers Stoke Sharks 8-4. Mike Hart (Sharks) made a 30 break in his drawn game.
Karl Cake’s double enabled Portchester X to defeat Waterlooville D 7-5. Neil Turp got the X men off to a good start before Craig Skeggs cancelled that out to draw level.
Last man Carl Fuggle’s victory claimed a share of the spoils for Broadoak Dandy’s in a 6-6 draw against Cowplain Misfits.
Dandy’s had a good start thanks to Eddie Orsmond, but Misfits hit back through Ray Houghton and Steve Dewhurst.
Waterlooville Bananas made the most of home advantage against Alexandra Bowls Club in the only League D fixture. There were wins for Wayne Rendle, Ozzy Rendle, Ollie Rendle and Dan Lee, with Paul Taylor grabbing a consolation double.
Report by Steve Toms