Totters crept up to 26-2 but Brian Wood and Rehman began to prosper, taking the score to 56, at which point the latter retired hurt.
A flurry of runs and wickets saw Totters finish on 178-6, Weston finishing unbeaten on 53.
Graham Millward took 5-46 and Mark Elvidge 3-31 as Totters
were restricted to 118-9, Brian Wood hitting 49 and Mohammed Kamren 47 - and then Brit Dutta slammed an unbeaten 74 as Dunlop stormed home for the loss of only three wickets,
The paceman, taking over the skipper's role from Mick Beale, produced a devastating individual performance to send visiting Totters to an emphatic 96-run defeat.
In reply, Totters resembled their name as wickets fell at regular intervals, Sayed (4-12) providing the perfect foil for the on-fire Davies, who blasted out the visiting middle and late order in devastating fashion to finish with brilliant figures of 6-20 in just 47 deliveries.
Totters were skittled out for just 33, Davies becoming the first Ansley bowler since Mick Hubbard in June 1985 to take a hat-trick for the senior side and the first Ansley captain since 1990 to get his side away to winning start in the league, Totters being the victims on that occasion as well.
And whether he opts for soft-spoken laments or kicks up a cloud of dust, Escovedo totters
on the brink of the abyss, wrenching out emotions like he's wringing a wet rag dry on ``With These Hands'' (Rykodisc).
Newly-promoted MSA Totters are one of several clubs confident of making an impact in what was formerly the top flight of the Coventry and District League.
Totters, who will be led by Brian Wood, will be looking to Richard Stuart to capture the wickets and Guy Weston to lead the chase for runs.
Totters, one of three clubs to be promoted after last year's champions Offchurch were moved up to Division Three along with Newdigate and Atherstone, open their programme at Ansley tomorrow.