Unbeaten Albion had to bounce back against Plymouth after falling behind in the 12th minute to a strike from Jamie Mackie.
Shelton Martis grabbed the equaliser before Cech, who joined Albion in a £1.4million deal from Porto last summer, struck his first goal for the club in spectacular style five minutes before half-time.
Cech then sealed Albion's success with a neat 83rd minute finish to move Roberto Di Matteo's side a point clear of Newcastle United at the top of the table.
But the win only served to add to the increasing problems of Plymouth manager Paul Sturrock.
His side remain without a win this season and have now collected just two points from six games.
Things could have been different if Gary Sawyer had not missed a sitter when Plymouth were 1-0 up.
But Sturrock knew his luck was out when Karl Duguid crashed a shot against the bar in the 52nd minute before a brilliant one-handed save by Scott Carson denied Cillian Sheridan just two minutes before Cech's match clinching second.
Plymouth had been justifiably rewarded for a fine start when Alan Gow created the opening goal for Mackie.
Gow, who was impressive all match, picked out Mackie on the edge of the Albion area.
Mackie was tracked by Martis but easily brushed aside his challenge and powered towards goal.
Even then, the threat appeared minimal as Mackie was left with an acute angle, but somehow his weak close range shot slid under Carson at his near post.
Plymouth should then really have doubled their advantage ten minutes later when Mackie turned provider.
His flick found the unmarked Sawyer just eight yards from goal but he wastefully headed wide with Carson stranded.
That near miss finally sparked lacklustre Albion into life and they drew level when Plymouth goalkeeper Romain Larrieu failed to collect a 34th minute corner from Graham Dorrans.
The cross flew over Larrieu and presented Martis with the simple task of stabbing the ball into an empty net from two yards as he made amends for his earlier error.
Plymouth's early confidence disappeared after Martis struck and Albion took full advantage to take the lead through Cech.
Roman Bednar set-up the Slovakia international with a neat lay-off and Cech let fly with a dipping 25-yard drive that gave Larrieu no chance.
Cech then completed his brace from close range when he converted a cross from the hard working Graham Dorrans.