Basement club Leicester had gone eight league matches without a win prior to picking up maximum points against both West Ham and West Brom, with those results lifting the King Power Stadium outfit within three points of safety.
Indeed, a three-goal winning margin for Leicester on Saturday, coupled with Burnley failing to win at Everton, would see them climb out of the relegation zone, as fellow strugglers Hull City and QPR are not in action this weekend.
"We've given ourselves a more realistic chance, but we've got to keep producing," said Pearson. "Our home form must improve and we have to stay focused.
"We've got almost the entire first-team squad available, which is important going into the run-in.
"We've had some bad luck, but the belief of the group has kept us going. It takes courage to keep standards high.
"We've got to make sure our run-in is what we want it to be. Our performances must be what we expect of ourselves.
"Other results only matter if you do your own job. If we can apply pressure by improving our own chances, all well and good."
Swansea have a dismal record when it comes to matches played in Leicester and are without a win in 10 since their last victory at Filbert Street in 1950.
The Welsh club equalled their Premier League points record of 47 with a 1-1 draw at home to Everton last time out, but will need to avoid defeat at Leicester for the first time since 1980 if they have designs on surpassing that marker this weekend.
"Playing any team is hard in this league, but the intensity of a team fighting for their lives at the end of a season is even harder," said Swansea boss Garry Monk.
"To be honest, I'm surprised they are where they are. I've watched them this season and they have some great quality. They've been unlucky with some results.
"But they have got themselves into a better situation with their last two results, so it will be another three points for us to fight for.
"Getting level with the points total is great, but I want to beat it."
Nelson Oliveira or Marvin Emnes look set to get the nod up front for Swansea, with Bafetimbi Gomis sidelined for up to four weeks with a hamstring injury, while Neil Taylor's two-match suspension presents Monk with a defensive dilemma.
