The Bees almost went ahead in the ninth minute when Brett Johnson's untimely slip let in Lee Roach, but Nikki Bull got down well to save at the striker's feet. Ten minutes later Underhill erupted as Ben Strevens gave Barnet the lead after finishing a neat move.
Nick Bailey picked out Roach, who in turn fed Richard Graham. The winger jinked his way into the box before firing a low cross into the Aldershot penalty area for Strevens to hammer home his second goal of the season.
The Shots also had their chances when Jon Challinor pulled off a neat turn on the edge of the box before bending his shot goalwards only for Barnet keeper Scott Tynan to parry into the path of Adrian Caceres, who was also denied by Tynan.
Giuliano Grazioli doubled Barnet's lead in the 59th minute after Graham had worked his way down the left flank before crossing for him to steer the ball past Bull for his 21st goal of the season.
But the league leaders have been careless of late, and they were guilty of another lack of concentration when on-loan striker Jake Robinson pulled a goal back for the Shots. The Brighton man poked home from close range after a Tim Sills knockdown.
Barnet were then reduced to ten men after Dean Sinclair was given his marching orders. Having been booked for a foul in the first half, the midfielder reacted angrily to a foul by Sills and was shown a second yellow following a push on the striker.
Aldershot pressed forward and in the dying moments could have earned a share of the points when Scott Rendell's header hit the post and bounced clear, but the Bees clung on to their lead.