David Greenhill opened the scoring on the half-hour then doubled his tally. Shire's third came in the last minute when a Greenhill effort was deflected into the net by Elgin's Paul McMullan.
Albion Rovers are a mere goal behind East Stirling as they too kept their 100% record with a 3-0 win against Clyde. Gary Phillips' eighth-minute strike put Rovers ahead before Pat Walker doubled their advantage.
In the 37th minute Phillips netted again.
Stirling Albion complete the trio of sides on maximum points after a 2-0 success against Peterhead. Dale Fulton netted Stirling's opener in the 27th minute and Phil Johnston's 25-yarder sealed the points.
Annan Athletic earned a 2-1 success over Montrose at Galabank. Goals from Kenny McKay and Stephen Black were enough for Annan, though Montrose's Garry Wood pulled one back from the penalty spot.
Bottom-of-the-table Queen's Park were thrashed 4-0 by Berwick Rangers at Shielfield.
Michael Keenan's own goal handed the lead to Berwick. Scott Dalziel added a second and Darren Lavery's second-half double saw off Queen's Park.