College of Engineering, Guindy established in 1794 by British colonialists as School of Survey
Thomason College of Civil Engineering, 1847, the oldest autonomous engineering school in Asia
(now known as Indian Institute of Technology, Roorkee (IITR)), attained university status in 1949.
College of Engineering, Pune (COEP) was established in 1854 as School of Mechanical Engineering,
Bengal Engineering College, established in 1856, is the second oldest (considering the year of graduation)
and one of the premier engineering institutions in India
Deccan College (Pune) established in 1821.
University of Mumbai is one of the first three oldest public state universities in India established in 1857.
Technically, UM offers engineering degree through affiliate colleges.
Indian Institute of Science, Bangalore (IISc) established in 1909 by J.N. Tata (famously called 'Tata Institute' by locals)
The University Visvesvaraya College of Engineering, Bengaluru is affiliated to Bangalore University and was established in 1917.
Indian Institute of Technology Varanasi (IIT BHU) established in 1919 as Benaras Engineering College. For more details, see Gaurav Ranjan's answer.