The criminal on the run managed to _____ capture by the police officer.

The sentence describes a criminal avoiding being captured. 'Evade' means to escape or avoid, especially by cleverness or trickery, and it directly takes 'capture' as its object. 'Invade' means to enter forcefully, which doesn't fit. 'Slip' and 'run away' would need additional prepositions to fit grammatically. Hence, 'evade' is the correct choice.