UNH is now 1-8 while UConn remains unbeaten at 10-0.
Henderson scored what proved to be the game-winning goal at 28:00 when she gave the Huskies a 1-0 lead with a low, hard shot from the middle of the circle. She also scored goals in the 40th and 65th minutes.
Laura Puddle, who finished with two assists, extended the visitor's lead to 2-0 just 56 seconds after she set up Henderson's first tally of the game.
UConn took that two-goal lead into halftime. Henderson's second tally was followed by one by Lizzy Peijs at 50:10 to give the Huskies a 4-0 advantage. Peijs struck again at 67:32 to cap the scoring.
UNH goalkeeper Christine Buckley (Walpole, Mass.) made 11 saves to mark the fifth time in 10 games this season she has reached double digits in saves. Melissa Bostwick stopped two shots defending the Connecticut goal.
One of the Wildcats' best scoring chances came in the opening minutes of the game. With Bostwick drawn from the goal line, a shot by Kaitlyn Skelley (Wolfeboro, N.H.) was blocked by UConn defender Brianna Clark.
New Hampshire returns to action Oct. 3 (1 p.m.) at the University of Maine. The next Wildcats' home game is Oct. 6 vs. Dartmouth College. Game time at Memorial Field is 7 p.m.