Christian Doidge's first goal for Newport County AFC wasn't enough to secure victory at Rodney Parade as the Exiles paid the price for some poor finishing and one defensive lapse.
County remain unbeaten at home under new manager Hayden Mullins but have now gone five games without a win since their impressive 3-0 opening-day rout of Rochdale.
They have at least put another point on the board after successive away defeats at Salford City and Northampton Town, but they will feel it could have been so much more after an excellent first-half display.
Mullins made two changes from the 1-0 defeat at Northampton, welcoming back Doidge from injury and handing deadline-day loan signing Michael Adu-Poku his first start.
Yahya Bamba and Kieron Evans made way as top scorer Shaquille Gwengwe moved back out wide to allow Doidge to lead the line.
Adu-Poku impressed the Rodney Parade crowd with his hard work in attack and defence on the right wing, and was the subject of some rough treatment from the visitors as a result, while Doidge could easily have opened the scoring inside two minutes.
There were just 73 seconds on the clock when Harrison Biggins crossed for the striker, who got the ball trapped under his feet and the chance was gone.
There was a chance at the other end three minutes later when Harrison Neal's shot was saved in an unorthodox manner by Jordan Wright, who scooped the ball over the bar with his forearms.
And County wasted another great opportunity to seize the initiative in the 14th minute when Cameron Norman crossed from the right and Kyle Cameron sent a free header over the bar from eight yards out.
The Exiles continued to probe and really started to step up the pressure on Fleetwood in the final 10 minutes of the half.
Great footwork from Matty Jacob inside the area teed up Matt Dibley-Dias for a shot at goal and his goal-bound effort was blocked in front of the line before Norman skied the rebound under pressure.
Dibley-Dias then dragged another shot wide from the edge of the area before County broke the deadlock seven minutes before half-time.
It came from a fantastic move down the left flank as Cameron played a defence-splitting ball inside the full-back for Jacob to run on to and cross for Doidge to tap in from close range.
The 34-year-old front man jumped for joy as the emotion of scoring his first goal in amber shone through.
And Doidge looked in the mood to make up for lost time after the break as he hit the post, admittedly when the flag was up, and then sent a diving header just wide from a Biggins free-kick.
Adu-Poku also has a shot easily gathered by Jay Lynch, but Fleetwood weathered the storm and snatched an equaliser in the 68th minute when substitute Aaron Loupalo-Bi diverted in a low cross at the near post.
Mullins immediately sent on Bamba and Evans in place of the tired, bruised and battered Adu-Poku and Gwengwe.
Joe Thomas, Tanatswa Nyakuhwa and Matt Smith also entered the fray in the closing stages but County couldn't force a winner.
County (4-2-3-1): J Wright; C Norman, L Jenkins, K Cameron, M Jacob (J Thomas, 82); C Brennan, M Dibley-Dias (M Smith, 89); M Adu-Poku (Y Bamba, 69), H Biggins, S Gwengwe (K Evans, 69); C Doidge (T Nyakuhwa, 89)
Substitutes not used: J Turner, D Sassi
Fleetwood (3-1-4-2): J Lynch; S Rooney, R Bennett, F Potter; H Neal; R Cirino (D Andrew, 57), A Murphy (J Robertson, 79), M Helm (C McLean, 57) L McCann; C Evans (W Davies, 63), R Coughlan (A Loupalo-Bi, 63)
Substitutes not used: J Pradic, J Dempsey
Booked: M Helm, F Potter, C Evans, S Rooney, R Bennett
Referee: S Singh Gill
Attendance: 4,178
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