To give the slip means to get away from somebody without that person knowing about it till (perhaps) at a later time.
1. The thief threw sand in the policeman's eyes and gave him the slip.
2. Despite the numerous security guards posted at the White House, the couple managed to give them the slip and gatecrash the party hosted for the Indian Prime Minister.
3. Aditya very smartly managed to give his father the slip and ran out to play with his friends.