Nicky Forster's first goal since his return to Brentford earned The Bees a point against Exeter City.
The Grecians looked as if they had snatched three points as they hung on to an early goal.
Brentford were totally dominant, particularly in the second half, and time after time the visitors were reliant on goalkeeper Paul Jones or the rub of the green to keep their sheet clean.
But four minutes into stoppage time Forster forced home a corner so the game finished 1-1 and The Bees had something to show from a fine attacking display.
The visitors could scarcely have made a better start - taking the lead inside 100 seconds.
The ball was played into the space behind the Brentford defence and Craig Woodman slipped on the rain-soaked pitch as he went to turn and retrieve it, John O'Flynn was on it like a flash, took a touch and drilled it past Richard Lee into the bottom corner.
Liam Sercombe curled an effort wide as Exeter tried to build on the early goal but Brentford soon recovered and played most of the match on the front foot.
Matt Taylor made a vital clearance for the visitors as Charlie MacDonald looked set to find Karleigh Osborne six yards out and Paul Jones tipped a looping defensive header from Billy Jones over his own crossbar.
Marc Laird elected to try and find MacDonald rather than shoot from 18 yards after a Gary Alexander knock down and Myles Weston blasted wide soon after.
Lee saved a low Daniel Nardiello shot and Troy Archibald-Henville headed a corner wide when well placed but Brentford held the upper hand.
Laird curled an effort just wide from 25 yards and Richard Duffy made a vital deflection to divert a Michael Spillane cross away from Weston.
MacDonald had a looping header saved as Brentford piled on the pressure, forcing numerous corners and putting dangerous balls into the penalty area.
The Exeter goal was leading a charmed life - Paul Jones made a fine low save when MacDonald drilled in a shot after picking up a Woodman pass, the ball broke to Laird, who reacted quickest and got off a left foot shot with the ball spinning away from him and players closing in that cannoned off the post.
The second half started as the first had ended, Weston saw a deflected effort loop over and Alexander headed a Laird corner wide.
Spillane saw a shot blocked when a Laird corner reached him at the far post and Alexander forced Paul Jones into a low save.
Exeter showed notice of their threat on the break when a Jake Thomson cross narrowly eluded Nardiello and Lee had to be quick off his line to reach a through ball before the speedy Thomson seconds later.
Paul Jones saved another looping Laird effort as Brentford continued to press and it just looked a matter of time until The Bees equalised, with Spillane proving particularly effective as an additional attacking option on the right.
Marcus Bean came within a whisker of levelling when he turned a deep Woodman cross into the side netting from a tight angle and Paul Jones saved a low Weston shot soon after.
The Exeter goalkeeper was the busiest man on the pitch, and was also getting the rub of the green and he saved a Laird shot and saw it bounce back to him as it ricocheted around the box.
But he earned his luck moments later when he tipped a MacDonald shot onto the crossbar and away to safety.
The visitors were hanging on by the fingernails - time after time the ball bounced around the penalty area with Brentford unable to get the vital touch.
But they also had menace on occasional breaks forward - Spillane had to be alert to block a Scott Golbourne shot after a good raid down the right by O'Flynn.
Bean shot over after a nice break forward, Alexander saw a header deflect over and MacDonald failed to turn in an Osborne nod down from a Laird corner.
Weston shot wide and Laird nodded a Woodman cross wide as the minutes ticked by while at the other end Lee saved from Golbourne and Jamie Cureton shot over as Exeter looked for the second goal that would have sealed it.
And Lee made a vital save from James Dunne after a break into the box to keep The Bees in it.
Brentford introduced Robbie Simpson and Forster in an attempt to salvage something but it appeared Exeter had weathered the storm.
However, with time running out, MacDonald won a corner he had no right to on the far side, Woodman floated it in, Pim Balkestein nodded down and Forster forced it in.
The Bees defence still had to be alert to block in the dying seconds from Cureton to ensure they took the point.
Brentford: Lee; Spillane (sub Wright 90 mins), Osborne, Balkestein, Woodman; Laird, O'Connor, Bean (sub Simpson 74 mins), Weston (sub Forster 83 mins); MacDonald, Alexander
Subs (not used): Royce, Bush, Diagouraga
Exeter City: P. Jones; Duffy, Archibald-Henville (sub Tully 64 mins), Taylor, B. Jones; Sercombe, Dunne, Noble; Thomson (sub Golbourne 69 mins), O'Flynn, Nardiello (sub Cureton 78 mins)
Subs (not used): Krysiak, Cozic, Stewart, Logan
Bookings: Duffy (33 mins), Nardiello (64 mins)
Attendance: 4,767 (557 away fans)
By Chris Wickham