Accrington went in front early on through an unfortunate own goal from Morecambe centre-half Henry McStay but the Shrimps came roaring back.
They dominated most of the game and Craig Stanley levelled the scores with a deflected free-kick early in the second half.
Accrington started the game much the brighter and were rewarded with an early goal.
With just five minutes played the on-loan Terry Gornell crossed, the ball took a slight deflection and McStay was caught out, the ball coming off him and beating Barry Roche for the opening goal.
The Shrimps should have been 2-0 down only four minutes later when John Miles beat the offside trap and had acres of space but his pass failed to give Terry Gornell the easy finish that it should have.
After the let off the Shrimps were soon on the front foot themselves and amazingly hit the crossbar twice in a minute.
The first was in the 17th minute when, after excellent play in the midfield, Ryan McGivern slid the ball across for Stewart Drummond and he looked certain to score but his shot cannoned off the bar and his effort on the rebound was deflected wide.
From the resultant corner by Craig Stanley, Aaron Taylor produced a smart snap-shot that also crashed into the crossbar with Kenny Arthur in the Stanley goal well beaten.
With Stanley heading over and Rene Howe directing a header straight at Arthur, the Shrimps were very much on top with Accrington not threatening Roche's goal.
The second half brought better news for the Shrimps as after only five minutes Stanley fired them level when his curling free-kick flew into the top corner after taking a slight deflection off an Accrington head.
Accrington came back into the game for a short spell but Roche was not needed as the nearest the visitors came was a shot from James Ryan that flew well over.
As the game headed into the final 20 minutes play was wide open with neither side seeming to have the edge - the Shrimps having more of the ball but Stanley looking dangerous on the break.
Drummond had another go from distance but the clear-cut opportunities that had arrived regularly earlier on proved harder to come by and both teams had to be content with a point.