Daggers stormed ahead in the 14th minute when Montano exchanged passes with Josh Scott and unleashed a fierce drive past Barnet goalkeeper Dean Brill from 20 yards.
Barnet created a number of opportunities to equalise, but Izale McLeod, Sam Deering and Alassane N’Diaye all shot wide.
On the stroke of half-time Daggers doubled their lead. Kevin Maher’s chip into the box was flicked on by Brian Woodall into the path of Montano, who blasted into the top corner.
Daggers came close again in the 59th minute when Dominic Green’s 25-yard strike bounced back off the crossbar before Woodall wrapped up the points in the 63rd minute when his diving header from Montano’s right-wing cross nestled into the bottom corner.
Barnet continued to press forward late on, but McLeod’s shot was smothered away by Daggers goalkeeper Chris Lewington and substitute Charlie Taylor headed over N’Diaye’s cross from close range.