It was not that long ago that the Toffees were in danger of being dragged into the relegation battle, but three wins and a draw in their last four outings have turned the team's season around, leaving them 12 points clear of 18th ahead of this match.
Everton were disappointed to concede a season-half equaliser to Swansea City in their 1-1 draw at the Liberty Stadium last time out, but the draw extends their unbeaten run, which stretches back to before the international break.
Everton will fancy their chances of extending that run this weekend, as they have lost just three times at Goodison Park this season, although they have drawn almost half of their 15 fixtures at home this campaign.
Martinez has been full of praise for goalkeeper Tim Howard during the week, with the American having kept eight clean sheets in the league so far this season - more than a number of sides above them in the table, including Tottenham Hotspur and Stoke City.
Scoring goals has been something of an issue for the team though, as they have found the back of the net just 40 times, which is just twice more than 18th-placed QPR.
However, they have been more of an attacking force in recent weeks, scoring in each of their last four matches after a run of just two goals in the five matches before that stretch.
Everton have a mixed run between now and the end of the season, hosting Manchester United and Spurs in their remaining games, while also facing the likes of Sunderland and Aston Villa, who still need points to make sure they are in the top flight next season.
Recent form: LLWWWD
Recent form (all competitions): WWLWWD
Sean Dyche's side come into the match sitting in the relegation zone, but they know that a win at Goodison Park could be enough to lift them out of the bottom three, particularly with QPR, who sit just above them, not in action this weekend.
Burnley have shown that they are capable of fighting for their place in the top flight in recent weeks, following up a win over Manchester City last month with a goalless draw against Spurs, but they were narrowly beaten by Arsenal last weekend.
Finding the back of the net has been a major issue for the Lancashire side in the league this season, with Burnley scoring more than once just six times, and just once since their 1-1 draw with Chelsea back in February.
Burnley can be a stubborn defensive side though, keeping seven clean sheets - the same number as West Ham and Spurs - while letting in 50 goals, which is one fewer than Newcastle.
If they can keep their focus in the final weeks of the season, they can still avoid the drop as they face a number of the teams around them, including Leicester City and Hull City, with ninth-placed West Ham the trickiest fixture remaining.
Recent form: LLWLDL
Meanwhile, Burnley have rarely made changes to their starting lineup this season, having stuck with the same XI for the match against Arsenal last week after drawing with Spurs the week before.
The club have reported no fresh injuries from the defeat to the Gunners, so Dyche will have the option to select the same players again for this match.
Everton possible starting lineup:
Howard, Coleman, Stones, Jagielka, Baines, Barry, Lennon, McCarthy, Osman, Kone, Lukaku
Burnley possible starting lineup:
Heaton, Trippier, Duff, Shackell, Mee, Boyd, Arfield, Jones, Barnes, Vokes, Ings
Head To Head
When the sides met at Turf Moor earlier in the season, Everton came away with a comfortable 3-1 win, with Samuel Eto'o scoring twice in his brief spell with the club, while Lukaku was also on the scoresheet.
When Burnley were last in the Premier League in the 2009-10 season, each side claimed one win, with Everton beating their opponents 2-0 in the last meeting at Goodison Park.
Neither side has dominated this fixture in their 77 previous meetings though, with Burnley winning 22, Everton claiming 31 and 24 resulting in draws.
We say: Everton 2-1 Burnley
Everton have been in impressive form over the last month and the return of Lukaku should give the home side more firepower going forward. Burnley will not make it easy, but the hosts should have enough to secure all three points.