The midfielder was joined by Tom Huddlestone - who completed his transfer to the Tigers alongside Jake's loan move last week - with Steve Bruce's team 2-0 down at half-time.
Hull performed well in the second half as the scoreline stayed 2-0.
Bongani Khumalo played 90 minutes as Doncaster recorded a first win back in the Championship after promotion with a 2-0 success against Blackburn Rovers on Friday night. They now play highly-fancied Wigan on Tuesday.
Grant Hall, Massimo Luongo and Alex Pritchard all started and played 90 minutes as Swindon suffered a 2-0 defeat at Shrewsbury in League One on Saturday.
Adam Smith was an unused substitute as Derby lost 1-0 at home to Leicester City.