The Lions looked set to collect their first win in nine attempts – and their first under interim boss Neil Harris – as they led 2-0 through goals in each half from Lee Gregory and Aiden O’Brien.
But Brentford, also desperate for points at the other end of the table to maintain their promotion bid, pulled one back through Alex Pritchard’s penalty before Odubajo snatched a 2-2 draw at the death.
Millwall, looking revitalised since former striker Harris took over from Ian Holloway earlier this month, threatened first after just two minutes when Ed Upson found Martyn Woolford, whose shot from the edge of the box was parried by David Button.
Brentford almost went ahead after 15 minutes through a glancing header from Spanish midfielder Jota, but the ball cannoned back off the crossbar.
And in the 28th minute Millwall got their noses in front when Gregory latched on to Upson’s long ball over the top, rounded Button and fired into an empty net from 15 yards.
It was the former Halifax striker’s sixth goal of the season and, tellingly, only Millwall’s 14th away from home during a troubled campaign.
Brentford poured forward in search of an equaliser before half-time but found Lions keeper David Forde in inspired form, the Irishman tipping a Stuart Dallas curler over the top, blocking a header from Jonathan Douglas and turning Pritchard’s free-kick around the post.
Brentford continued in the same vein after the interval but Andre Gray fired over and Sid Nelson bravely blocked Jota’s shot.
And the Bees were hit by a sucker punch midway through the second half when O’Brien played the ball out to Woolford, continued his run forward and nodded the winger’s lofted cross into an empty net from a yard out for his first senior goal.
But Brentford were offered a lifeline with six minutes remaining when Woolford tripped Alan Judge in the area and Pritchard rifled home the penalty.
And in the first minute of injury time, with Millwall pegged back in their own penalty area, right-back Odubajo fired through a crowd of players to snatch a dramatic equaliser.
There was still time for substitute Gary Taylor-Fletcher to win it for Millwall, but the striker’s shot flew agonisingly wide to leave the Lions players with their heads in their hands.
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