The Linnets headed to Garden Walk to take on newly-promoted Royston Town top of the early-season table, having won five of their six matches.
But two second half goals for the Crows condemned Lynn to their first defeat.
Scott Bridges broke the deadlock after 72 minutes, and 9 minutes later, Adam Marriott doubled the home side`s lead and end the Linnets unbeaten start.
Slough Town and Kettering Town now top the fledgling table after Tuesday wins.
The Rebels enjoyed a sixth straight league win at Arbour Park against Hitchin Town, whose slow start to the season continues.
It was a good night for James Dobson, who netted a hat-trick in front of 442 with goals in the 24th, 71st and 75th minutes.
Simon Dunn wrapped things up with a fourth for Slough 8 minutes from time.
he Poppies edged out St Ives Town by the odd goal in seven at Westwood Road.
St Ives scored within seconds of the kick-off through Danny Kelly.
Kettering then equalised within 90 seconds with a goal from Ben Milnes and by the 10th minute were 2-1 up through Brett Solkhon.
The second half saw four more goals in the gale force wind and rain, with Kettering going 3-1 up through Michael Richens only for Kelly to bring it back to 3-2.
Solkhon also scored his second to make it 4-2 before Kelly completed his hat-trick to set up a tense finish, but the Poppies held on to take the points.
A goal in each half enabled relegated Bishop`s Stortford to register their first win of the season to date at the ProKit Stadium against Kings Langley.
The Blues first goal in the 26th minute came when Darren Foxley ran through the middle after collecting Dipo Akinyemi’s through pass and beat keeper Ross Hampton with a low drive – Stortford’s first goal in almost six hours of football.
Jason Williams netted number two in the 64th minute and that proved enough for Bishop`s Stortford to get up and running.
In contrast, another relegated side, Gosport Borough, were condemned to a seventh straight defeat – this time 4-2 at Privett Park against promoted Farnborough.
Alex Pike’s men remain rooted to the bottom of the table after falling 4-0 behind inside the opening 24 minutes to goals from Dan Walker and Connor Calcutt topping and tailing a Jamie Cureton brace.
Aaron Dawson reduced the deficit after 28 minutes and Gosport `won` the second half with an 81st minute Luke King effort, but the damage all came in that bad opening period.
Dunstable Town are also yet to record a win, and were beaten 2-0 a The Meadow by Chesham United.
The Generals` third win of the campaign to date came courtesy of an early 5th minute lead from Oran Swales and a late Scott McGleish effort 9 minutes from time.
Another excellent crowd of 2,005 saw promoted Hereford FC make it four wins from seven after a 5-2 Edgar Street success against Stratford Town.
Garyn Preen gave the Bulls a 28th minute lead that Mike McGrath added to within 4 minutes.
A second for Preen 2 minutes later and one from Gethyn Hill on 39 minutes took the Bulls into the break 4-0 up.
Ben Stephens eventually reduced the arrears in an understandably low key second half in the 79th minute and cut it further 2 minutes later before Mike Symons made it a nap hand for Hereford 5 minutes from the end.
Tiverton Town, promoted with the Bulls, earned a 2-1 Ladysmead win over Weymouth.
Levi Ladricombe put the Yellows in front 3 minutes after half-time and then Jamie Short added a second after 66 minutes.
Jordan Rose pulled one back for the Terras with 8 minutes left to play, but Martyn Rogers` side held firm to record victory against one of his former clubs.
Banbury United were well beaten by an impressive Redditch United side at the Spencer Stadium.
The Reds went into the break two-up with goals from Dior Angus after 24 minutes and Spencer Weir-Daley 7 minutes later.
Danico Johnson eventually made the points safe for Darren Byfield`s side with a third 15 minutes from time, although record-breaker Jefferson Louis maintained his scoring run with a consolation 2 minutes into stoppage time.
Sam Smart bagged a brace as Basingstoke Town recorded a 2-0 Camrose victory over Merthyr Town.
Smart eventually broke the deadlock in the 67th minute and then added his and `Stoke`s second 10 minutes later.
BY STEVE WHITNEY