Manny Aybar followed with a go-ahead bloop into left and Shuck later added an insurance RBI as Los Angeles completed a four-game sweep of Kansas City with their eighth straight overall win.
Jerome Williams (4-1) earned the decision, allowing two runs on seven hits over six innings. He walked two and struck out four.
Ernesto Frieri picked up his 10th save to secure the Angels' triumph.
Davis (3-4) was saddled with the loss, yielding three runs on six hits over 6 1/3 innings.
David Lough got Kansas City's only RBI.
Jessica Simpson shares three-way kiss with friends in photo
Interpol investigating stolen passports on missing flight