But the Londoners had to withstand a last 20-minute barrage from the Essex side and also saw Damion Stewart sent off.
The defender launched into a two-footed tackle that sent Mark Yeates sprawling as the U's piled on the pressure.
Sub Luke Guttridge had a right-foot shot well saved by Lee Camp and Clive Platt sent a tame header into the grateful arms of the Rangers keeper.
But there was nothing Camp could do when just after the hour Platt nodded on and Yeates caught the Rangers' defence dithering to nip in and chip his eightth goal of the season.
Colchester also hit the post when a speculative cross from Danny Granville was dropped by Camp and back into play, with no-one able to capitalise.
The U's resurgence came after Rangers had dominated the first 50 minutes and deservedly raced into a two-goal lead.
It looked all over when Buzsaky was on the end of a slick three-man move to slide the ball under Dean Gerken on 52 minutes.
Before that the Hungarian warmed up a tepid first-half affair with a superb left-footed strike from the edge of the box beyond Gerken to put Rangers ahead.
Rowan Vine ploughed a fertile furrow down the left flank for Rangers, but his best effort in the first-half was a hammered strike from 15 yards which the keeper did well to palm over.
Twice more the loan forward delivered telling crosses with no team-mate able to get on the end.
Colchester's best effort was a dipping free-kick from Johnnie Jackson saved down low by the agile Camp.
But the U's cause took a down turn when Kemal Izzet was forced to go off holding his wrist following a crunching tackle with Bob Malcolm.
Colchester recovered to finish the stronger team, only to lose out on what would have been a deserved share of the spoils.