With nine of Tony Carr's team involved in Wednesday's hard-fought FA Youth Cup victory over Norwich City, there were understandable signs of tiredness, and Spurs made full use of their extra sharpness.
After a fairly even opening to the game, the visitors opened the scoring on the half hour mark and didn't have their lead threatened before the interval.
Hammers made a more positive start to the second half and added a much-needed spark but, after Greg Pearson missed a glorious chance to level the scores, they found it difficult to break down a well-organised Spurs defence.
Neither side created any clear cut chances as the game drew to a close, but in the dying seconds Spurs broke on the counter-attack and added a second to make sure of the victory.
Said Tony Carr afterwards: "We lost to the better team today and I have no complaints with the result.
"We had a lot of tired legs after Wednesday night. That isn't an excuse, but we did lack sharpness and Spurs were just too strong for us on the day.
"We needed that goal to lift us early in the second half, but we just couldn't do it and Spurs deserved their victory in the end."
Team: Jackson, McClenahan (Khan 55), Tattum (Blewitt 55), Ferdinand, Ward, Lumsden, Noble (Morris 55), Carrick, Cole, Pearson, McMahon. Subs unused: Sealey, Fletcher.
Meanwhile, the under-17s could only manage a 0-0 draw at home to Coventry City - their first goalless stalemate of the season.
After an evenly-matched first half, Hammers dominated the second period and missed a couple of decent chances to secure all three points.
In the end they had to settle for a share of the spoils, but Kevin Keen was pleased with his team's first clean sheet since October.
"It was disappointing not to take all three points, but the clean sheet was a bonus and there were some other positives - not least the performance of young Chris Cohen, a young schoolboy defender, who was outstanding.
"With another schoolboy, Mark Noble, having played for the reserves in the week, our next batch of Academy scholars certainly look promising and it bodes very well for the future.
"The draw was the least we deserved today, although Darren Behcet made one outstanding save to deny them in the first half."
Team: Behcet, Wright, Parrington, Henry, Cohen, Collington (Shaw 65), Tucker, Bunce, Welsh, Lee (Yao 75), Allen. Subs unused: Reed, Singh.