Scott Boden, Haydn Hollis and Jak McCourt also found the net as Town remain unbeaten in four matches under manager James Rowe.
The win takes the Blues up to 15th and leaves them just four points off the play-off positions.
Hollis, Whelan, McCourt and Asante all shone in what was a ruthless team performance.
Here are Liam Norcliffe’s player ratings from the game...
1. Kyle Letheren 7
Third clean sheet in a row for Letheren. He didn't have much to do but he made a good double save towards the end. Photo: Rachel Atkins
2. George Carline 7
Started at right wing-back on his home debut just like he did against Sutton. Carline saw a lot of the ball in the first half but Barnet closed him down well. After the break, he was much more effective as Town found him free in space. He almost scored with one powerful drive before being replaced by Cropper with 25 to go. Photo: Dean Atkins
3. Josef Yarney 7
Came in for the suspended Will Evans on the right of a back three. A steady performance. Photo: Steve Flynn/AHPIX LTD
4. Haydn Hollis 8
Four starts under Rowe and four solid performances. Looks a totally different player. Another top display rounded off with his second goal in as many games. Photo: Dean Atkins