O'Hare hammered home an equaliser deep into injury-time at the ADT Stadium to stretch their unbeaten BetVictor Northern Premier League South East Division run to 12 games.
Manager Graham Drury admitted his side had been 'really lethargic' in the first half before producing a strong response after the break.
They found themselves trailing to Rob Norris' 55th minute opener for Dynamo before finally breaking the home side's stubborn resistance.
Drury said: "We were really lethargic in the first half. Everything was slow and pedestrian. We didn't move the ball quick enough.
"They responded really well to everything I asked of them at half-time though. Loughborough scored totally against the run of play.
"We had penetrated their 18-yard box perhaps five or six times before they scored.
"They made it very difficult for us once they scored and we had to throw the kitchen sink at them.
"I am so proud of Dec because he's a top player trying to get into a good side. It's been difficult because the lads have been in great form.
"I still felt the goal was coming, but I couldn't see where it was coming from. The change of pattern by pushing Rob Morgan wide has paid off because Dec's been slipped in down the side and it's a good finish from a good player.
"Loughborough deserve credit because they made it really tough for us. They were sharper in the first half and had a little bit more zip about them without really causing too many problems.
"They defended really well, but it's always a tough place to come. This keeps our unbeaten away run and the point was so important because it keeps us clear of the sides chasing us."
Stamford made one change to the starting line-up which had demolished Glossop North End last weekend with Cleveland Taylor coming in for the injured James Blunden who faces a few weeks on the sidelines after chipping a bone in his foot in the previous match.
Jordon Cooke was moved into the heart of the Daniels defence alongside skipper Sean Wright with Taylor coming in at right-back.
Clear-cut chances were few and far between in the opening period with neither keeper seriously tested.
The best chance of the first half fell to the hosts just a couple of minutes before the break when Alex Steadman set up Danny Gordon who blazed over when well-placed in the Stamford box.
Stamford started the second half on the front foot and top scorer Tom Siddons was denied by a brave save from imposing Dynamo goalkeeper Jason Alexander who saved at close range following Taylor's pinpoint through ball.
Alexander again thwarted a decent Siddons strike moments later before the hosts broke the deadlock after 10 minutes of the second period.
Burrows' free-kick into the Stamford penalty area saw Rob Norris react first and his glancing header nestled in the bottom corner past the diving Dan Haystead.
Stamford responded rapidly as Morgan's low cross was spilled by Alexander but the Dynamo defence reacted first to scramble clear.
Karl Demidh then had a shot well blocked by Haystead with Gordon dragging the follow-up wide.
Demidh fired wide of the far post after being set free by Charlie Scanlon before Stamford started to ring the changes in a bid to force an equaliser.
They had a flurry of corners which almost brought a leveller as Harry Vince's flag kick was diverted goalwards by a Dynamo defender only for Charlie Young to produce a crucial clearance off the line.
Will Norcross stabbed another shot wide for the hosts while any Stamford response could only find the grateful arms of Alexander.
Just when it looked like Stamford's impressive away record would be shattered, O'Hare popped up with a dramatic equaliser with virtually the last kick of the game.
Morgan's slide-rule pass found the Stamford substitute racing into the box and he produced a calm and composed finish to rifle past Alexander and spark wild celebrations among a strong and vociferous away following.
The draw leaves Stamford in second spot, two points behind league leaders Leek Town, ahead of their next test on New Year's Day when Wisbech Town are the visitors to the Zeeco Stadium (kick-off 3pm).