Every point is precious for Paul Clement's charges and the side from south Wales had cause for celebration last weekend as Gylfi Sigurdsson's superb late free-kick earned the Swans a share of the spoils against Manchester United at Old Trafford.
As a result, Swansea are just two points adrift of safety with three matches remaining and Clement's team will be acutely aware, with two home matches left, that they must maintain their solid form at Liberty Stadium if they are to stand any chance of beating the drop.
The Swans have been beaten in just one of their last six Premier League matches in south Wales - a 3-1 defeat to title-chasing Tottenham Hotspur last month - and the odds compilers offer 9/5 (2.80) that Clement's charges claim a vital victory against Ronald Koeman's men.
Everton have enjoyed a decent campaign and the men from Merseyside will be determined to put the disappointment of last week's 3-0 thumping from league leaders Chelsea behind them as they target a finish in the top six of the Premier League standings.
The Toffees, though, have a poor record on the road. Koeman's side have failed to come out on top in any of their last six Premier League away fixtures and bet365 offer 6/4 (2.50) that Everton buck the trend with a win in Wales and 9/4 (3.25) that the match ends all square - a selection that would have landed in four of Everton's last six Premier League encounters away from Goodison Park.
Everton have been in free-scoring form at home this season, but the Toffees have looked like a different team on their travels. The visitors have scored more than once in just one of their last seven matches on the road - a stark contrast to their record of 28 goals in their last nine home matches in the Premier League.
Swansea's bid to preserve their Premier League status has been bolstered by the collection of four points from their last two matches, but the nerves are sure to be jangling this weekend and a tight, tense tussle looks like a probable outcome.
There have been more than two goals scored in just one of Swansea's last seven Premier League matches, while there have been fewer than three goals scored in five of Everton's last seven matches away from home. Indeed, the Toffees' most recent match on their travels finished 0-0.
There could, therefore, be value in backing fewer than three goals to be scored at 19/20 (1.95) ahead of Saturday's showdown in south Wales.