West had struggled early on but Alastair Storie stopped the rot in company with Gregor Maiden and Alan Williamson, with whom he added 81 in 17 overs to take his team to 190.
Storie remains, technically, the best batsman in Scotland and his 58 was a polished knock which mixed solid defence with some fine drives and cuts.
Mohammed Ramzan got Poloc off to a promising start but, after he fell foul of the medium-paced swing of John Cameron, Spence put up the shutters to grind out an unbeaten 38 and force the draw.
RHSM took advantage of West's inability to win to join the Glasgow team at the top by beating Carlton. Having batted over to top 200, they seemed to have let Carlton back into the game at 146 for five. But Craig McKellar ripped out four batsmen in three overs and finished with six for 72 as the visitors crashed to 168 all out.
Aberdeenshire maintained their 100 per cent record in Conference C with an easy eight wicket victory over Uddingston at Mannofield and Ayr climbed into second place with a hard-fought win over Greenock, thanks largely to an unbeaten century from Kevin Roberts, who also claimed three Greenock wickets.
Arbroath secured their third win of the season when Freuchie collapsed to 79 all out in the face of some excellent bowling by Neil Burnett (5-23) and Zahid Mohammed (4-7) and strolled home for the loss of one wicket.
Heriot's edged ahead in Conference A in bizarre fashion. West Lothian's late arrival at Goldenacre - their fixture card showed it as a home game - and eventually bad light halted proceedings after only 75 overs. That rendered the game void so Heriot's retained their 100 per cent record.
Hillhead claimed a thrilling first win when they took Dunfermline's last wicket with three balls remaining.