Shaun Loft was absent for the clash as he served the final match of a three match ban after being sent off in the previous round, but there was a debut for Jamie Crellin after signing from Worthing.
United found themselves a goal down within the second minute after a break down in communication allowed a long goal kick to reach Theo Woodhouse , who slotted home past a stranded Grant Young.
United ressponded quickly and Jason Taylor was inches away from drawing United level but his goal bound header was saved on the goaline. Wes Tate also came close moments later after good work by Ryan McBride, but United had to wait until the 15th minute to draw level.
A surging run from Jack Divall was brought to an abrupt end inside the penalty area and gave Tate the opportunity to draw United level from the penalty spot, which he duly did.
Luke Denton could have given United the lead on 23 minutes but his volley cleared the crossbar from six yards out following a Tate corner.
Young was forced into a smart save to deny Woodhouse as Chessington pushed for a goal, but Crellin nearly opened his tally on the stroke of half time with a 30 yard effort that cannoned off the crossbar.
Grant Harrison saw a glancing header go narrowly wide at the start of the second half, moments before Chessington were reduced to ten men after a reckless lunge by Jaz Gold on Tate.
United made their numerical advantage count six minutes later when Jason Taylor made space on the edge of the area to place his effort past the `keeper and give United the lead.
The lead lasted just eight minutes however as substitute Tommy Harper slid home past Young after a drilled cross from the right wing.
Four minutes later, neat interplay from Tate, Matt MacLean and Jack Franklin played in Scott Dartnall who produced an inch perfect cross to McBride, who beat the advancing `keeper to the ball as the ball nestled in the bottom corner of the net.
Chessington pushed forward in the hope of securing an equaliser as Woodhouse and Moralley both brought out the best in Young. Woodhouse also hit the bar with a 25 yard effort and saw another disallowed as it proved to be United's day as they progressed to the Third Round on Saturday 7th December