A third wicket stand of 145 between Nathan Round (72) and Matt Pardoe (92) laid the foundations for Kidderminster to reach 240-7 from their 55 overs.
In reply, Berkswell collapsed to 50-7 before a rearguard action from Grant Thornton (33) and Tom Milnes (32) brought a recovery.
The recovery, though, was short-lived, as Berkswell slumped to 106-9 with Liam Weston (3-20) shining with the ball for Kidderminster.
However, a brave last wicket stand, by Joshua Aspinall (10no) and Adnaan Riaz (8no) took them to 124-9 at the close.
That denied Kidderminster an opportunity to close the gap even more at the top – with Neil Pinner's side currently sat second in Division One, 19 points behind Berkswell.
Smethwick have dropped to fifth in the table after being beaten by Knowle & Dorridge.
Knowle & Dorridge opening batsman Alex Phillips followed up his century last weekend with another ton.
Phillips (118) and Amir Khan (81) put on 202 for the first wicket as K&D marched to 271-6 after 55 overs.
Gurinder Singh (4-85) was the most impressive bowler for Smethwick who lost two early wickets in reply.
Hamza Ahmed and Aman Hussain, both scored 48, but Smethwick crumbled to 146-9.
That made it seem as though Knowle & Dorridge would secure an emphatic win.
They were denied, however, by an unbeaten 31 from last man Naseer Ahmed who took the score to 179-9 at the close with the support of Zayan Kayani who finished unbeaten on five.
The match between Walsall and Shifnal was declared void because of Covid issues in the Shifnal camp.
In Division Two, league leaders Halesowen were beaten by local rivals Harborne in a game dominated by the bowlers.
After winning the toss and opting to bat first in sweltering conditions, Harborne made a poor start, slumping to 40-4 with all four wickets falling to Eddie Rhodes.
Rhodes, then took a well-earned rest as Halesowen concentrated on containment with Alexei Kervezee and Peter Scott bowling 28 overs of unthreatening off-spin to a defensive field.
This enabled Tom Payne (50) to lead a recovery with help from Jack Holloway (31no), Jimmy Clifford (29) and Tejas Wagle (28) as they reached 167.
Rhodes then returned to the attack and quickly polished off the tail with Harborne all out for 190 in the 52nd over.
That left Halesowen 58 overs to reach their target.
But missing three key players, they made a slow start to their reply, scoring at two runs per over for the first 25 overs.
The run rate picked up when Kervezee (37) came to the wicket and after surviving a confident appeal for caught and bowled, he appeared to have reignited Halesowen’s challenge for victory.
Off-spinner Swapnil Gugale (4-44) posed the main threat for Harborne, but it was the return of the seamers Payne (3-12) and skipper Tom Arnold (3-44) that proved decisive as Halesowen were dismissed for 146 in 55 overs.
There was better new for Himley who picked up 20 points by securing a straightforward win over Oswestry.
Himely travelled to Shropshire and dismissed the home side for 159 with Matt Jeavons (3-36) posting their best bowling figures.
The visitors were then guided to a five wicket victory thanks to a composed 73 from Callum Lea.
Rock bottom Pelsall were yet again on the wrong side of a close finish as they were beaten by Kenilworth Wardens.
Wardens closed on 199-9 after their 55 overs. But Pelsall fell 13 runs short on 186.
Batting second, Pelsall reached 67-2before Jake Lee was out for 46.
But Alex Jones continued the fight until he ran out of partners. Jones finished unbeaten on 67 but, in the end, his efforts proved to be in vain.
The match between Wolverhampton and Barnards Green was declared void due to Covid issues.