Sidwell deservedly handed the Championship winners the lead with a thumping header after 25 minutes.
Irishman Doyle then made it two from the spot after being hauled down by Carl Hoefkens, before Adam Rooney's close-range finish gave Stoke hope.
But Halls turned in Stephen Hunt's pass to put the hosts on 102 points - three short of Sunderland's record.
Stoke acting first team coach Noel Blake:
"I thought we did better than in the defeat to Southampton on Saturday.
"In the first half we were slightly off the pace but in the second we were a lot better although we switched off at the back for their third goal.
"Reading are champions and that's because they are a very, very good team. They fight for each other and fill in for each other."
Reading: Stack, Shorey (Golbourne 64), Makin, Sonko, Halls, Ingimarsson, Sidwell (Dobson 54), Gunnarsson, Hunt, Doyle (Cox 71), Long.
Subs Not Used: Hahnemann, Kitson.
Goals: Sidwell 25, Doyle 56 pen, Halls 62.
Stoke: Simonsen, Hoefkens, Dickinson, Duberry, Hill, Mbuyi, Kopteff (Rooney 45), Brammer, Russell, Sweeney (Gallagher 51), Bangoura (Henry 71).
Subs Not Used: de Goey, Broomes.
Goals: Rooney 59.
Ref: S Mathieson (Cheshire).