Spurs started on the front foot and things were made extremely difficult for Colchester inside the first five minutes when centre-backs Tom Eastman and Alex Wynter clashed heads. Eastman had to go off for stitches and was eventually substituted midway through the half, while Wynter was treated by paramedics and left the pitch on a stretcher.
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Jake Kean was called into action to deny Christian Eriksen and Nacer Chadli after a lengthy stoppage, while Erik Lamela beat the U's keeper but not the post as the Argentine's curling effort struck the woodwork.
Harry Kane and Eriksen both missed the target before the first goal eventually came in the 27th minute as Chadli, on his 100th Spurs appearance, found the far corner from the edge of the box - his third goal in as many games.
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Spurs continued to dominate in the remainder of the first half, but they could not double their lead as Kane headed at Kean with an excellent chance shortly after Chadli's goal.
Colchester managed to keep the lead at just one as six minutes of added time were played before Spurs picked up where they left off at the start of the second half, with Lamela curling wide with two good chances.
The hosts' best spell of the match followed as Darren Ambrose and Gavin Massey threatened, but it was Spurs who scored the second goal to pour cold water on any hopes the U's had of mounting a comeback.
Moments after Chadli had struck the bar, Eric Dier tried his luck from distance and had his shot wickedly deflected into the far corner by Matthew Briggs, leaving Kean no chance of saving it.
Colchester had a golden chance to halve the deficit when substitute Marvin Sordell was played through on goal and struck the outside of the post.
That miss was made doubly bad moments later when Chadli met Kieran Trippier's cross from the right to make it 3-0.
Colchester pulled one back soon after as Gavin Massey's shot came back off the post and hit Ben Davies to cross the line, but Spurs quickly restored their three-goal lead as Tom Carroll poked home a Chadli cross from close range.