Priestley helped Shelf recover from a perilous 95 for five with a unbeaten 115 as the visitors racked up 264 and Dean Smith's men emerged one-run victors.
It completed a miserable weekend for Bradshaw, who were top of the Premier until being bowled out for 51 and humiliated by Northowram Hedge Top on Saturday.
Priestley, who had made 72 in the win over Augustinians eight days earlier, slammed nine sixes and eight fours to put Bradshaw on the back foot. He figured in stands of 77 with Shiv Hadimani (22) and 63 with Craig Green (26).
Bradshaw lost James Marris for 30 with the total on 80 but a second wicket stand of 141 between Chris Soulsby (96) and Wayne Cotton (66) put the hosts in a strong position for a late push. However, Shelf held their nerve to claim their biggest scalp since joining the league last year.
Another ex-Bradford Central League side, Jer Lane, also knocked out a top section side in Booth.
New skipper Jim Mosley hit 93 at the top of the Booth order but the other early order batsmen struggled and it needed 30 from Nigel Horsfall and 26 from Gareth Swaine to help them to 205 for nine.
That sort of total does not faze a Lane side who won Division Two last season and are going great guns in the middle section this time.
Swaine sent back the top four batsmen but a stand of 125 between Jason Gelder (97) and Chris Ramsden (39) took them to the brink of victory.
Both fell to Oliver Collinge with the total of 203, Gelder having hit 14 fours and three sixes.
Copley won at Sowerby Bridge in the only all-Premier Division tie, their experienced attack soon getting on top against a home side lacking the Whitehill brothers.
Shakar Saghir's 48 helped lift the home total from 62 for five to 169 and he also grabbed a couple of wickets as Copley threatened to let a solid start slip, Chris Goulden (30) and Tim Rushton (34) having put on 63 for the first wicket.
However, Craig Chew's 38 not out and Peter Hoyle's 18 not out saw the visitors to the winning post.
SBCI openers Jamie Summerscales and Alex Kaye figured in their second massive opening stand of the season to put the skids under Clayton.
Having put on 224 to help floor champions Mytholmroyd on the opening day, this time they took the total to 318 before Kaye finally departed for 142, a knock which included 15 fours and one six.
However, Summerscales went on to reach 201 not out, hitting 24 fours and seven sixes in a total of 350 which proved far too many for Division Two outfit Clayton, whose 144 included 54 from opener Howard Stead.
Two other opening batsmen to make hay in the sunshine, as the first Halifax League bowl-offs were averted, were Triangle's Nathan Madden (141 no) at home to Outlane and Sowerby's Adie Gawthrope (148 no) against visitors Low Moor.
There was also an unbeaten 103 for King Cross's Iqbal in a 103-run win at Queensbury while Dean Crossley (123) and promising young quick bowler Tom Bellfield (six for 21) helped Southowram to their anticipated easy win over Stainland.
Jon Lord made a fine return from suspension with 45 runs and five wickets as holders Mytholmroyd beat Old Town.

REVISED SECOND ROUND DRAW: Southowram v Copley, Jer Lane v Warley, King Cross v Old Crossleyans, Triangle v Shelf, SBCI v Northowram HT, Bridgeholme v Blackley, Old Town or Mytholmroyd v Oxenhope, Sowerby v Greetland.push.