Record signing Platt, snapped up from MK Dons for £300,000, had the last word - slamming in the equaliser in the 89th minute as the U's hit back for the second time.
Colchester, with the evergreen Teddy Sheringham starting his 24th season, following his free transfer move from West Ham, matched the promotion favourites in the opening minutes, midfielder Kevin McLeod trying his luck with a low drive, blocked in a packed goalmouth.
Lee Hendrie, a summer capture from Aston Villa, battled in midfield but United struggled to find a way through a tough Colchester side which flirted with the play-offs last season.
Keith Gillespie almost found a way through in the 19th minute with a teasing corner cleared by George Elokobi, before Colchester almost found a way through in the 26th minute.
Mark Yeates, snapped up from Spurs for £100,000, swept past Hendrie before curling over a low cross from the right flank, toe-poked inches wide by Platt.
Colchester forced two quick corners, the second from Johnnie Jackson deceiving the United rearguard as Paddy Kenny punched the ball clear from under the bar.
James Beattie, United's £4 million record signing from Everton, finally got the better of marker Pat Baldwin as he stretched to meet a Gillespie corner, but his header lacked punch as Dean Gerken snatched the ball on the line.
The hardworking Hendrie was set up by Beattie minutes after the restart, as he took a stride before drilling in a low strike from 15 yards, the ball flashing inches wide of Gerken's left-hand post.
Colchester almost snatched the lead on 51 minutes after winning a free-kick 30 yards out, Jackson hitting a searing shot towards the top corner as Republic of Ireland keeper Kenny pulled of a spectacular stop to palm the ball over.
United, stung into action, were foiled by the woodwork eight minutes later. Gillespie pumped over another inviting cross and Beattie connected, only to see his header crash against the bar and as Billy Sharp moved in, the ball was hacked away.
The breakthrough came in the 67th minute, full-back Derek Geary floating over a cross from the right as Beattie rose at the far post to beat Gerken with a textbook header from five yards.
Colchester were back on level terms straight from the kick-off as Yeates powered up the right flank before slamming in a low cross, finished off from close range by McLeod.
Substitute Michael Tonge hit United's second eight minutes from time after Gillespie's corner was only half cleared and the midfielder, lurking on the edge of the area, found the target through a packed defence.
However, Platt had the last word, finishing off from close range after United's back four failed to cut out Karl Duguid's deceptive cross.