Jimenez’s double took his tally to 11 for club and county in 36 appearances this season.
The 34-year-old had last scored against Manchester United in a 3-2 defeat on 1 February.
Jimenez, though, may have been fortunate to have still been on the pitch, having been booked in the first half for catching Ballard with a flailing arm and almost getting a second yellow card for the same offence on Omar Alderete a few minutes later.
In a drab game with few chances before his opener, Jimenez’s quality in the box sparked it into life.
He was denied a chance of a hat-trick when he was substituted for Rodrigo Muniz in the 65th minute.
Fulham boss Marco Silva was also forced into taking off Kevin, who picked up a muscle injury in the first half, having come into the team to replace the injured Samuel Chukwueze.
But Fulham still had an attacking threat and Wilson continued his fine individual form by assisting Iwobi’s late goal.
Since the start of November, only Erling Haaland (17) and Bruno Fernandes (15) have been involved in more Premier League goals than the Wales winger (7 goals and 5 assists).
Sunderland analysis: Consecutive home losses for Black Cats
Having started the season with an impressive 12-match unbeaten run at home in the Premier League, Sunderland have now lost their past two games at the Stadium of Light, failing to bounce back from their defeat to Liverpool.
Moments before Fulham’s opener, Romaine Mundle was played in by Lutsharel Geertruida, but he missed the target from only a few yards out.
Nilson Angulo also had an effort touched over the bar when Sunderland were trailing 2-0.
It was a frustrating afternoon for the Black Cats, made worse by two first-half injuries.
Manager Regis le Bris lost defender Nordi Mukiele – impressive this season – and Jocelin Ta Bi, who was making his first league start for the club.
But the sight of captain Granit Xhaka returning in the second half after a four-match absence was a welcome one as Sunderland look to halt a worrying run of four losses in five league games.
