Dyer and Vardy produced two top quality goals to enable Leicester to chalk up a record-breaking victory.
The 2-1 Sky Bet Championship win at Birmingham was Leicester's eighth successive success and also their fourth away victory on the trot - both new club records.
The latest success only exemplified their current status as favourites to win promotion.
Dyer, who is presently in the throes of negotiating an improved contract at Leicester, certainly enhanced his prospects with a vital first-half strike.
Vardy sealed the victory with a fine individual strike in the 83rd minute for his 10th goal of the season, although Leicester conceded an 86th-minute goal from Birmingham's Peter Lovenkrands.
The Blues' miserable home form continued and they have now failed to win any of their last nine games at St Andrew's.
It was always going to be a severe test for the young Birmingham side against high-flying Leicester and they gave a good account of themselves, particularly in the second half.
The supremely confident Foxes displayed their swift attacking skills in the early stages and Birmingham did well to hold the league leaders at arm's length.
Vardy was accorded Leicester's first goalscoring opportunity. The striker cleverly turned to create a better opening but his worthy effort was effectively blocked.
Birmingham, who last won at home back in September, were handicapped by the enforced absence of skipper Paul Robinson (suspended) and Matt Hancox (injured).
The result was a defensive dog-fight as Birmingham were relentlessly battered by a swift inter-changing Leicester attack.
Birmingham's resolution enabled them to survive the initial onslaught but their young midfield often came off second best against the dogged play of Danny Drinkwater and Matty James.
It was Drinkwater who tested Birmingham's goalkeeper, Darren Randolph, when he created an opening for himself only to see his on-target shot pushed away by the Republic of Ireland international.
But Randolph had little chance in the 24th minute when Leicester predictably took the lead through Dyer.
The goal was carved out by David Nugent, who has been outstanding this season with his ability to provide goalscoring opportunities besides being the Foxes' leading marksman.
On this occasion a low angled pass from the right found the unmarked Dyer who controlled the ball before lashing a powerful shot into the roof of the net.
Dyer then set up Anthony Knockaert but his close range shot from just five yards was blocked by Randolph with his legs.
The pace of Vardy always posed problems for Birmingham who were often at panic stations keeping out the lean and hungry Foxes in the first period.
Birmingham, not for the first time this season, played with more verve and imagination in the second half with the skill of Albert Rusnak and Reece Brown finally emerging against the league leaders.
But it was all in vein as Vardy produced a fine solo goal in the 82nd minute.
The confident striker collected a Riyad Mahrez pass and worked his way down the right, cleverly beating two defenders before scoring his with a low angled shot into the far corner or the net.
Substitute Lovenkrands then ensured an anxious final four minutes for Leicester when he headed home a cross from Chris Burke.