New £2million signing Clinton Morrison, back at Palace after his midweek transfer from Birmingham City, was given a standing ovation by the home fans before the start of the match, but Dowie kept him under wraps on the substitute's bench until the 75th minute.
By then Palace were stuck in a rut as they tried to hold on to Johnson's 44th minute goal and they looked to be going nowhere.
Morrison soon showed his class though, and within five minutes of coming on, he set up Johnson's second goal with a delightful one-two.
Johnson was left with just the goalkeeper to beat and he cleverly chipped his shot over the Stoke City shot-stopper Steve Simonsen.
The Potters must have been pleased with their first-half endeavours and their game plan to prevent Palace getting up a head of steam worked to a tee.
But just seconds before the break Tom Soares and Gary Borrowdale created an opening and, from Jon Macken's perfect flick, Johnson was left with a tiny bit of space to fire a brilliant 20-yard shot past Simonsen's left hand to put Palace one up.
However, instead of capitalising on this timely breakthrough, the Eagles were still finding it difficult to pin down the visitors. Meanwhile Stoke were eager to get back into the match and former Gillingham striker Mamady Sidibe was proving particularly menacing as he forced Gabor Kiraly to make a full-length save.
The Stoke striker then fired wide of an open goal and you could sense the Palace dug-out getting more agitated by the minute.
It was time for Morrison to make his entrance and produce the magnificent pass that allowed Johnson to finish superbly to finally kill off Stoke's challenge.