Kitson and Sherwood bagged the goals between them as the reserves failed to capitalise on periods of intense pressure to put the game beyond the Hammers.
The second string lined up in a 4-4-2 formation with Ciaran Toner, Alton Thelwell, Anthony Gardner and Ben Thather forming a protective wall in from of Kasey Keller.
Goran Bunjevcevic was the man in the mask in in central midfield alongside Tim Sherwood, with John Piercy and Matthew Etherington playing right and left respectively. Sergei Rebrov and Yannick Kamanan provided the spearhead.
After some enterprising early sparring the game certainly sprung into life on four minutes. Laurent Courtois flicked the ball to Paul Kitson who ran at Thatcher before dispatching a powerful drive past the helpless Keller.
The Spurs response was almost immediate, Etherington probed down the left and fed the ball to the on running Sherwood on the edge of the penalty area. Tim took aim and blasted a low right foot drive past Stephen Bywater in the Hammers goal.
Calderwood's boys were now on top, with Etherington dictating procedings, but it was Yannick Kamanan who attempted the audacious, attempting to chip Bywater with a first time effort on the turn from about 30 yards. Bywater was stranded but Yannick's effort floated just wide.
As they continued to press, Bunjevcevic was denied by Bywater, while Keller made a smart stop from Svetoslav Toderov at the other end.
On 20 minutes Bunjevcevic fed Etherington who dazzled the Hammers rearguard with his searing pace that led to him winning a corner. Matty flighted in an inviting outswinging corner and it was Sherwood who accepted the invitation, firing a bullet header past Bywater's right hand.
Spurs continued in much the same vein of domination early in the second period and Bywater was at full-stretch to deny Rebrov's point-blank header from seven yards.
As West Ham edged back into contention, Toderov fed Kitson through and Keller made himself big, reduced the angle and the former Derby man shot straight at him. Shortly afterwards a deflected Piercy effort landed on top of the crossbar.
With 65 minutes on the clock Sergei stung Bywater's fingers with a low piledriver as Spurs reclaimed the momentum after a brief spell of West Ham pressure.
The Hammers stepped on the gas as the game approached the final 15 minutes and Keller was forced into a vital stop after Kitson evaded both Gardner and Thatcher.
From the next move Sergei was denied with another header after Etherington controlled a high ball and swung over an inch-perfect cross which found Sergei unmarked six yards out. His downward header was somehow kept out by Bywater.
John Sutton replaced Kamanan for the last nine minutes, the 17-year-old given the opportunity in his first reserve start to play alongside Sergei, and he nearly latched onto a Sherwood through ball.
Two minutes from time a Courtois corner was headed down in the direction of Kitson who spun on the spot and planted his shot past the virtually unsighted Keller to level the scores.
Team: Keller, Toner, Thatcher, Thelwell, Gardner, Bunjevcevic, Piercy, Sherwood, Kamanan (Sutton 81), Etherington, Rebrov. Subs: Snee, Kelly, O'Donoghue, Consorti.
West Ham: Bywater, Johnson, Minto, Lomas (Britton 80), Potts, Foxe, Newton, McCann, Kitson, Toderov (Riza 68), Courtois. Subs: McMahon, U'Ddin, Ferrante.
A Tim Sherwood double was cancelled out by a late Paul Kitson goal that handed West Ham a share of the spoils after an absorbing contest at Broadhall Way.