The hosts made 209 for 8, with Aston falling just short on 189 for 8.
Elsecar were asked to bat first and in the first half of their overs found the going exceedingly difficult as they struggled to 53 for 4.
Then Glenn Yates and Shahzad Rana added 54 runs in the next five overs before Yates fell for 52.
Rana’s innings developed into a cultured knock until he fell at 70.
The Elsecar innings improved to 209 for 8 at the end of their overs, while Aston’s South African Juan Grobbelaar was impressive with 4for 26 and Usman Azeem supported with 3 for 57.
Aston Hall chased the total well, with opener Joe Barker notching 33 and Amir Riaz 36.
The issue looked in doubt with Aston needing 70 from their final 10 overs, with four wickets remaining and with the menacing Grobbelaar leading the chase.
Elsecar’s relief was tangible when Ifzal bowled Grobbelaar when he had scored 36 from 34 balls and Aston settled for two bonus points.
Division One’s Aston Hall B lost out to Norton Woodseats.
Aston batted first and Tim Shaw (53) and the early order batsmen built a promising base at 144 for 3.
Aamir Ashfaque had been introduced into the attack however and he proceeded to waltz his way through the remaining batsmen claiming 6 for 42 in the process.
Aston lost their final seven wickets for just 19 runs and were 163 all out.
Abul Khayer also took 3 for 20 for Norton.
Aston claimed early success and the first three Norton batsmen retired with just 14 runs between them.
Michael Burney (55), Shahzad Hussain (46) and Ashfaque (37*) took up the cause and saw the visitors home by five wickets.
Jamie green took 3 for 35 for Aston.
In Division Four Maltby B were well beaten by Doncaster Town C.
The men from Finningley made 154 from their innings, despite the efforts of Michael Cannadine (5 for 34).
In reply, Maltby struggled from the outside and were eventually bowled out for just 97 runs.