Rubuta ci gaba ga wannan sakin layi - A 1987, Palmer yayi magana da shugaban McLaren Ron Dennis game da zama direban No. 2 na ƙungiyar don ninka Gwarzon Duniya Alain Prost. Dennis a karshe ya sanya hannu kan Stefan Johansson, kuma Palmer ya shiga Tyrrell mako guda kafin tseren bude kakar a Brazil
Ka yi haƙuri. Ko da yake ya wuce ta da turbocharged fafatawa a gasa, Tyrrell ta halitta-aspirated Cosworth-powered mota tabbatar da abin dogara, kuma shi ne nimble a tighter circuits. Palmer ya sami maki a gasar a tsere uku, kuma a gasar Grand Prix ta Ostiraliya ne ya kammala aikinsa mafi kyau a matsayi na hudu. Ya kuma lashe Jim Clark Cup, gasar zakarun Turai ga direbobi na motocin da aka saba da su. Ya zauna tare da Tyrrell na tsawon shekaru biyu masu zuwa, lokacin da mafi kyawun sakamakonsa ya kasance sau biyu na 5 da kuma sau uku na 6. A ƙarshen 1989 ya sanya hannu a matsayin direban gwajin McLaren.