The lift is provided by the rotors only. The rotors are powered by Rolls-Royce T406 engines, which are turboshafts: all useful generated turbine power is converted into shaft power for the rotors. Note that turboprops do convert some of the exhaust energy directly into propulsion thrust, turboshafts do not.
All helicopters can provide enough rotor thrust to lift their own weight plus that of (internal or external) payload. Wikipedia lists the max. VTOL weight as 23,859 kg, about the same as the CH-47 Chinook double rotor helicopter at 22,680 kg. The Chinook rotors are indeed longer and therefore require less power to generate the same amount of thrust: 4,590 kW for the V-22, 3,529 kW for the Chinook.