The 0-0 score will suit United more but Chelsea can count themselves unlucky not to take a first leg lead to Old Trafford.
First up for United was Argentine defender Gabriel Heinze who managed to get to the ball after Frank Lampard weaved his way through the defence on the left. His low right-footed drive beat goalkeeper Tim Howard, but Heinze was on the line to clear.
The second last-gasp stop came six minutes from time. Substitute Jiri Jarosik was free wide on the left inside the penalty area and his shot was beaten out by a combination of Howard and Phil Neville.
United defended like Trojans and clearly were able to carry out the game plan from Sir Alex Ferguson.
Chelsea for their part could have had the game sewn up by half-time.
Damien Duff saw his long run on 12 minutes end with a blistering 20-yard left-footer which just failed to go inside the apex of crossbar and post.
Lampard's flicked, glancing header on 29 minutes beat Howard but the ball inched past the stopper's right-hand upright.
United had a couple of penalty claims dismissed by referee Neale Barry. The first happened when Louis Saha seemed to be upended by Tiago. The second was more dubious as Cristiano Ronaldo appeared to slip following a challenge by John Terry.
Eidur Gudjohnsen had the ball in the United net on 30 minutes but was offside.
Wayne Rooney, back after a three-match ban, saw his goal-bound header well saved by Carlo Cudicini on 39 minutes.
Another Lampard drive was just wide on 58 minutes but the Londoners could not pierce the United rearguard.
It's all to play for in 14 days time for the return leg.