Cardiff ended a four-match winless run with a 1-0 triumph at St Mary's Stadium last weekend, a result that moved the Welsh side to within three points of safety.
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"Results change moods in football. Last weekend did just that," Solskjaer told reporters. "We need to build on the momentum [of] that win. There's a lot of belief that we can get the job done.
Solskjaer knows it will not be easy, though, as Stoke head to Wales in great form. The Potters beat Newcastle 1-0 last week to keep up a great run under Mark Hughes and sit inside the league's top half.
"We play a team that are in top form," he added. "They've won five in seven and are safe this season. They'll play with a freedom and confidence."
Cardiff goalkeeper David Marshall has urged his side to win two league games in a row for the first time this season, with five of their six previous victories followed by a defeat.
"We've not had back-to-back wins all season. That's something we want and need to do to put us in a good position," Marshall said.
"Last weekend was perfect. It gave us belief we perhaps didn't have after [the loss to Crystal Palace]. Back-to-back wins are now the aim. We need to come out of the traps quick but Stoke are in good form and will be tough.
"We needed a perfect weekend last time out and got it. We're more than confident that we can get the job done [and stay up] with four games left."