Poole score - Iam Middlebrook
Paul Hughes` side were beaten 2-1 by another side fancied to do well again this campaign, Metropolitan Police.
Herson Alves gave the hosts the lead from the penalty spot after 12 minutes.
Immediately after half-time, Cole Brown pulled Hayes & Yeading level.
But on 82 minutes, youngster Jasper Mather won it for the Met.
Bracknell Town, runaway winners of the Isthmian League South Central title and then switched by the FA in the summer, have also been tipped to go well but had to make do with a point from a 2-2 Bottom Meadow draw with another fancied outfit, Weston-super-Mare.
Jordan Esprit after 5 minutes and Seb Bowerman 8 minutes later had the Robins two-up.
Crucially, Dayle Grubb reduced the deficit from the spot 4 minutes before the break.
And then just as it looked as though the home side were going to begin life at Step 3 level with a victory, sub Ben Griffith popped up with an equaliser for the Seagulls 7 minutes into stoppage time.
The division’s other newcomers had mixed fortunes.
Plymouth Parkway, tipped by many to make it back-to-back promotions after winning the Division One South last season, were also held to a 2-2 draw at Bolitho Park by Chesham United.
Jeanmal Prosper gave the Generals a 17th-minute lead that Jordan Edwards doubled on 52 minutes.
But Ben Seymour bagged a brace in the 63rd and 80th minutes to salvage a point for the Devonians.
However, there was no joy on the opening day for the other three promoted teams.
Hanwell Town, who came up from the Isthmian South Central with Bracknell, lost 3-1 at home to Truro City, whose Will Dean gave them an early 4th-minute lead.
Tyler Harvey added a second right on half-time and debutant Ben Adelsbury made it 3-0 in the 55th minute, with sub Adam Laaref reducing the arrears on 68 minutes with his first touch.
Division One Central play-off winners North Leigh lost 2-1 at the Avenue Stadium to Dorchester Town.
Only 4 minutes had gone on the clock when Alfie Stanley gave the Magpies a lead that he doubled after 23 minutes.
Ben Brown headed the Millers back into the game 8 minutes into the second half but the hosts hung on for the opening day spoils.
Division One South play-off winners Winchester City were beaten 3-0 at home by Poole Town.
Goals from big summer signing Wes Fogden and Declan Rose had the Dolphins 2-0 up before Toby Holmes added a third in the second period.
The day’s other winners were Gosport Borough, Swindon Supermarine, Yate Town and Salisbury.
Gosport edged out reprieved Merthyr Town by the odd goal in five at Privett Park.
Harvey Bradbury gave Boro a 33rd-minute lead that Tom Handley cancelled out right on the stroke of half-time.
Abdulai Belle-Baggie restored Boro’s lead on 54 minutes and added a second and the home side’s third after 67 minutes.
An own goal 5 minutes later gave the Martyrs hope, but Gosport hung on.
Swindon Supermarine enjoyed a good 3-0 success at the Memorial Playing Fields against Hartley Wintney.
A James Harding penalty gave `Marine a 20th-minute lead and the Row suffered another blow on 38 minutes when they had Anis Nuur dismissed for a reckless tackle.
Just 3 minutes later, Tom Sharpe made it 2-0 and Conor McDonagh added a third in the 81st minute.
Yate began with a 1-0 success at Silver Jubilee Park against Hendon.
A goal from debutant Brandon Smalley after 37 minutes eventually proved enough for the Bluebells.
Salisbury also secured a one-goal victory on the opening day at the Ray Mac against Beaconsfield Town.
Ben Thomson scored the only goal 6 minutes into the second half.
The game at the Ian Moorcroft Stadium between Tiverton Town and Harrow Borough finished 0-0.
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