The Seagulls were without four players through injury, with Chris Noone (knee) and Jack Truelove (knee) hurt in the Boxing Day game and joining Marc Williams and Moustapha Saiel on the sidelines.
With Anthony Stephens also now back with Wrexham, manager Frank Sinclair had to bring in four reserve team players to make up the numbers.
Rob Hopley played at centre back in the first half and did well, but the team as a whole played poorly and Hyde hit the post and went close on a couple of other occasions, before taking the lead with a Ted Cribley goal just before half-time.
The manager then brought himself on and looked to have turned things around in the second half, which saw five goals scored in the last 20 minutes.
Sinclair headed the equaliser from a corner on 71 minutes and a minute later saw his side take the lead when Obi Anoruo shot on the turn past Hyde keeper Connor Hunt after a free kick had been played into him on the edge of the area.
The lead, however, lasted only five minutes before Hyde equalised, when a mishit Connor Hughes shot was turned in by Tom Bentham.
But the Seagulls then looked to have won it with a brilliant goal by Anoruo in the 85th minute.
He raced onto a terrible back pass to go round the keeper and then scored from an incredible angle near the bye-line to put the Seagulls 3-2 up.
Chris Sanna, returning in goal, made a couple of excellent diving saves, but deep into added time Cribley got his second of the game from a corner, with his shot taking a couple of deflections in a crowded goalmouth.
That gave Hyde only their second point in 13 away games this season, but Sinclair commented afterwards: “They are a better side than their position in the league suggests. I watched their game against Stalybridge the other day and they were unlucky to lose 4-2 in a game they could easily have won 6-4, and today was a similar thing.
“We had a patched up side and missed a lot of people who I believe would have made a big difference. We had to bring four reserve team players into the squad but managed to get something out of the game.
“I was certainly a lot happier at the end than I was at half-time. We weren’t at it in the first half and not enough players wanted the ball which was disappointing.
“I brought myself on because I felt I could influence more players to do their jobs better from on the pitch. To be fair we got a reaction in the second half, got ourselves back in it and the two goals by Obi were brilliant finishes which you would think would be enough to win the game.
“But it wasn’t to be and we didn’t have the best of luck with a couple of their goals.
“For their second the guy has scuffed his shot and it has gone straight to their striker, who I had left to try and block the original shot.
“Their third goal has taken two deflections and given Chris Sanna no chance with so many people around him, but I am disappointed that we had the ball in their corner with a minute and half to go and instead of keeping it there and seeing the game out we’ve let them come straight up the other end and force the corner from which they’ve scored.”
The manager added that he hopes that Noone and Truelove will be fit to face Stockport on Thursday and that Jordan Bove’s clearance will have come through to allow him to make his debut.
Colwyn Bay: Sanna, Taylor, Moss, Olapade, Royle, Hodgson (Watson 82mins), Haywood, Anboruo, Hopley, Mendes (Sinclair 45mins), Baynes. Subs not used: Ollerenshaw, Pilliner and Frost.