The former Chelsea hitman cancelled out John Akinde's 19th-minute opener for the hosts as they looked to get their promotion campaign back on track after a series of frustrating results.
Wanderers are fourth in the table, but a draw was not enough for Peter Taylor's ambitious side to climb into the automatic promotion places.
And Taylor will be frustrated that his team didn't make full use of home advantage at Adams Park, especially against a side struggling at the wrong end of League Two.
Loan Bristol City striker Akinde gave the hosts the perfect start, his thunderous drive being enough for the Blues to take the lead.
But Furlong beat Wanderers keeper Jamie Young with a clinical finish and the Bees stung their opponents when it mattered.
John O'Flynn went close for the visitors with a powerful strike in only the fifth minute, but Young saved well.
Akinde then broke the shackles for the hosts and they went in search of a second goal to secure maximum points.
However, it never came and, after some good pressure, Furlong levelled matters with a fine shot which left Young with no chance.
Gary Holt fired a shot straight at Barnet keeper Jake Cole on the hour mark, while Matt Harrold's last-minute shot was blocked by the keeper as Taylor's men were left frustrated.