But with two of the teams below them - Fulham and Cardiff - both winning last weekend, it has tightened things up in an increasingly frantic race to avoid the drop.
Swansea have successive home games against Aston Villa and Southampton following their trip to Tyneside, but Fulham's victory over Norwich three days ago and Cardiff winning at Southampton upped the ante.
Swansea skipper Ashley Williams: "It's impossible to know (what Swansea require from their last four games) because of what a strange season it has been, both at the top and the bottom.
"It is different to normal seasons as everyone is still in the mix. But we really need points.
"You always look at other results. That is normal, we are like anyone.
"You knew a day like Saturday was going to happen because teams are not going to keep losing every week.
Barclays Prem
11 West Ham 37
12 C Palace 37
13 Hull City 36
14 A Villa 34
15 Swansea 33
16 West Brom 33
17 Norwich 32
18 Fulham 30
19 Cardiff 29
20 Sunderland 25
"That day came and we knew this would be tough, but we have to concentrate on ourselves and if you are going to be in a relegation battle I would prefer to be in our position with points on the board."
Swansea have collected just nine points from a possible 30 since Garry Monk took on the club's head coach role in early February following manager Michael Laudrup's departure.
Williams: "It's just so bizarre.
"We train well, we set up well, we go out and do well most of the time and we create chances.
"I don't know. We are here and that is it. We have to fight, to keep working, but I am sure we will be okay with the fight we have shown and the people we have in the dressing room.
"We can't keep playing well for long periods of games and not win. We beat Norwich convincingly, we did well against Arsenal and we need more of those results.
"(Against Chelsea) (Wilfried) Bony and Wayne (Routledge) went close for us, and, I hate to say it, but it does seem like the luck is against us this season and the only way to beat this is to keep working hard."