Lynn lost their first away game since January as both sides had a penalty and had a man sent off.
It seemed as if the Linnets' fruitless record at the Hand Stadium would change after they were a goal up and Clevedon's keeper was red-carded within the first ten minutes.
The referee played a key part in the game, with Lynn's Steve Melton being dismissed for dissent.
Caretaker boss Shaun Carey said: "I can't believe we lost the game. We were totally in control in the first half.
"The ref evened things up, and it will be a massive blow losing Steve for three games.
"Steve said something to the player who fouled him, and the ref thought he was saying it to him.
"The ref said at half-time it was still a sending-off even if it was to their player, but if every player who swore was sent off it would be two v two.
"Both sides were down to ten men, and I felt we still had enough to have won the game."
Lynn, missing the injured Jack Defty and Rodney Hicks, looked tired after their recent cup exertions and after having a midweek cup tie on a heavy pitch.
But The Walks outfit began well as Matt Nolan had a shot in the first minute, but the ball was scrambled away.
The first talking-point of the match came when Michael Frew burst through from the halfway line, and home keeper Danny Greaves hauled him down. Greaves got a red card and Alex Notman sent Tom Jacobs, an outfield player deputising between the sticks, the wrong way for the spot-kick.
On the half-hour the referee spoke to Lynn skipper Mark Warren about the latter's constant complaining.
A minor episode perhaps, but it may have had some bearing three minutes later when Melton was tackled. He clearly thought he'd been fouled, and he was sent off for foul and abusive language.
Frew had a shot turned around the post, but as the game went on the sub keeper was not tested as much as he should have been.
In first half stoppage time what should have been a Lynn throw-in went to Clevedon, who charged upfield and won a penalty of their own when Grant Cooper tripped Jack Pitcher. Leon Hapgood converted the kick.
Shaun Marshall made some important second half saves, most notably from Mitchell Page, while Hapgood hit a post, and Billy Clark's flick was cleared off the line.
At the other end, on the hour a Cooper effort went just wide.
Pitcher put the hosts ahead with a grubber from a scramble on 71 minutes.
Lynn played three at the back (Warren, Charlie Defty and Mark Camm) and threw on two subs and had a reasonable amount of pressure.
But Pitcher nipped in for his second goal in injury time, latching on to a poor Charlie Defty back-pass to seal the game.
Clevedon: Greaves, Scott, Romhdane, Bater, Trought, Clarke, Hapgood, Mullings, Page (Sheppard 80), Pitcher, Haines (Jacobs 7). Subs not used: Rawlins, Murray. Booked: Romhdane 58, Hapgood 90. Sent off: Greaves 7. Goals: Hapgood 48 (pen), Pitcher 71, 90.
Lynn: Marshall, West (Norris 80), C. Defty, Warren, Cooper, Camm, Nolan, McMahon, Frew, Notman (O'Halloran 70), Melton. Not used: Harvey, Higgs. Booked: Nolan 80. Sent off: Melton 32. Goal: Notman 9 (pen).
Attendance: 207. Referee: D. Eaton (Gloucester). MoM: Shaun Marshall.
[Missing from report: O'Halloran booked after the match]