Chelsea had two opportunities to win the game at the death, but De Gea saved brilliantly from Mata in the last minute before parrying a fierce shot from Hazard in stoppage-time.
Indian-owned Blackburn Rovers earned an FA Cup quarter-final replay against Millwall after riding their luck in a 0-0 draw at The Den on Sunday.
Michael Appleton’s team were second best for long periods of the last eight clash between two out of form Championship clubs, but they enjoyed their share of good fortune to set up a replay at Ewood Park tomorrow.
Andy Keogh’s first-half header struck a post, before Lions striker Rob Hulse missed an absolute sitter from close range in the second half.
Rovers, owned by Indian poultry firm Venky’s, have endured a troubled season in the second-tier after last year’s relegation from the Premier League and Appleton is Blackburn’s third manager of the campaign. They did not have a shot on target against Millwall, yet are still in with a chance of a Wembley semi-final appearance thanks to their escape in south London.
Rovers stunned Arsenal in the previous round and are yet to concede in this season’s competition, but they found it hard going from the start.
Millwall had the ball in the back of the net when Keogh headed home Chris Taylor’s corner, but the whistle had already gone as Dany N’Guessan impeded goalkeeper Jake Kean.
Republic of Ireland forward Keogh then saw a diving header come back off the post as he connected with Jack Smith’s deep cross five minutes before the break.
Blackburn had a good chance to take the lead early in the second half, but Scotland striker Jordan Rhodes could only fire over after latching on to David Bentley’s set-piece.
Kenny Jackett’s Millwall kept pushing for the opener and Nigerian defender Danny Shittu unleashed a ferocious dipping strike from long range, which Kean tipped over for a corner.
The hosts should have been ahead moments later when Keogh’s ball across the face of goal picked out Hulse, only for the on-loan QPR striker to miscue his shot high over the bar.
Blackburn came back into the game as the second half progressed and Josh King saw a header come back off a post.
It was Shittu who went closest to taking his side to the last four, testing Kean again from long range, with the Rovers goalkeeper doing well to claw the rebound away from Hulse.