Rubuta ci gaba ga wannan sakin layi - A lokacin 2011 NHL Entry Draft
, Burns, tare da zagaye na biyu na zagaye a shekarar 2012, an yi ciniki da San Jose Sharks a musayar Devin Setoguchi, Charlie Coyle da zagaye na farko a shekarar 2011. Tare da shekara guda har yanzu a cikin kwangilarsa tare da Wild, Burns ya sanya hannu kan tsawaita kwangilar shekaru biyar a ranar 1 ga Agusta, 2011, tare da Sharks; yarjejeniyar za ta biya shi dala miliyan 28.8 a cikin shekaru biyar, tare da matsakaicin adadin albashi na dala miliyan 5.76. A shekara ta 2013, bayan da Sharks suka sayi mai tsaron gida Matt Irwin, a watan Maris, Burns ya koma gaba, inda ya ci maki 20 a wasanni 23 na kakar wasa. A cikin kakar 2013-14, Burns ya buga wasanni takwas na farko na kakar, amma ya rasa wasanni 13 bayan Oktoba 21 saboda ciwon gums. A ranar 21 ga Nuwamba, Burns ya dawo cikin jerin Sharks kuma ya zira kwallaye a kan Tampa Bay Lightning a cikin ƙoƙarin cin nasara 5<unk>1. A ranar 29 ga Nuwamba, a kan St. Louis Blues, Burns ya rubuta aikinsa na farko a cikin nasara 6 zuwa 3.