Ed Foster hit an unbeaten 105 to steer Shrewsbury to victory at York in the National Knockout quarter-final.
York made 205-7 in their 45 overs, but skipper Foster's knock saw Shrewsbury to 206-2 and a semi-final home tie with Chester-le-Street on 23 August.
Oswestry are 24 points clear at the top of the Shropshire Premier League after beating both Allscott and Welshpool.
Challengers Quatt were thwarted by rain against Much Wenlock on Saturday, and then drew with Allscott 24 hours later.
Mudassir Pasha was the hero for Oswestry, hitting 92 not out in the seven-wicket win over Allscott, and then taking four wickets as his side eased past Welshpool by 104 runs.
Following Saturday's wash out, Quatt were frustrated again on Sunday as they beat the weather but not their opponents.
Dean Robinson hit an unbeaten 98 as Quatt rattled up 234-4, but Allscott held on for a draw at 182-9.
Broseley (145-5) picked up 21 welcome points as they beat Welshpool (144-9) by five wickets in the only other Saturday game to survive the weather, while on Sunday Much Wenlock (96-8) saw off Ludlow (95) in a low-scoring affair, and Wem (109-9) beat Newtown (78).
Albrighton (129) and Madeley (129-9) tied their match.
The Birmingham League programme was completely washed out on Saturday.
That included Shrewsbury's Premier Division relegation clash at Leamington, leaving Shrewsbury stuck in second-bottom spot, 11 points behind their Warwickshire opponents and safety.