Rather than using burning extra fuel, Indian mission used a series of elliptical orbit raising maneuvers (Hohmann Transfer Orbit Maneuvers). This relied more on gravity than carrying more fuel and burning them to raise the orbits. It helped us save a lot of cost, though taking more time,effort and care. Besides, it was kinda the only option we had, as our launch vehicle, PSLV had limitations in the payload it can carry, and our GSLV launch vehicles, capable of carrying more payload had its own problems.
Sir isn't it the SLV and not the spacecraft which does the same?
A typical interplanetary mission uses a powerful rocket upper stage like the Centaur upper stage of Atlas 5 rocket, to kick the spacecraft directly into a transfer orbit to the target.
Centaur upper stage rocket, pushing a spacecraft into transfer orbit
ISRO's PSLV rocket could inject Mars Orbiter Mission spacecraft to an Earth orbit. But PSLV does not carry a powerful upper stage like Centaur to push the spacecraft into an interplanetary transfer orbit.
The mission design involving multiple firings, was developed to accommodate this limitation by making use of the same Liquid Apogee Motor (LAM) on-board the spacecraft, designed to carry-out the firing for insertion into the orbit around Mars.
In order to achieve the velocity required to escape from an Earth orbit, the relatively smaller capacity LAM engine has to be fired for a longer duration. But, the increase in velocity is achieved most efficiently when the firing is done at perigee - the point on orbit that is closest to Earth.
A series of perigee burns - 5+1 (supplementary) - were conducted - The aim was to gradually build up the necessary escape velocity of 11.2 km/s (7.0 mi/s) to break free from Earth's gravitational pull while minimising propellant use (because of firing done at perigee).
BUT Mars Orbiter Mission didn't use Gravitational Slingshot or Gravity Assist Manoeuvres to save fuel - It was a device called the
Ceramic Servo Accelerometer which did the same - An indigenous innovation from PRL, DoS - uses only a simple plastic mug and a Teflon wire “as the only investments” - The device weighs only 50 grams, not only saves fuel, but also measures acceleration, velocity and position of the spacecraft.
BTW - this is not the first time ISRO did try this innovative idea - they did the same with Chandrayaan-1 and the Ceramic Servo Accelerometer was first used on board the same - a more refined / upgraded version of the same was used on board Mangalyaan.