This match was the eighth and final one on a busy Saturday of Premier League action. It featured thrills and spills and nearly had a dramatic finish.
Villa defender Pau Torres twice had chances to snatch a late winner but failed to hit the target with close-range headers on both occasions.
After four games of this Premier League campaign, both of these teams were in the bottom three with one draw and three losses, and this draw maintains their recent resurgences.
Villa have now won three and drawn two of their five league matches since, while Fulham have picked up seven of a possible nine points in their past three games.
Jackson has had a fine October, with his goal following one in the 2-2 draw against Brentford, two in the 6-0 Champions League win over Fenerbahce and a double in the 2-1 win over Manchester City.
This encounter took place on Saturday evening rather than Sunday afternoon because Villa play in the Champions League at La Liga leaders Barcelona on Tuesday.
Some sides would be distracted by such a prospect, but Emery's Villa started brightly, with Goretzka heading one chance over.
His next header resulted in the penalty after Berge raised his arm.
The penalty was the first awarded to Villa in the Premier League since April 2025 against Manchester City, having not received one last season. Surprisingly, Jackson did not take it, and instead it was McGinn who took responsibility, only to hit the woodwork.
Suzuki, who joined Villa in a £30m deal from Parma in August, had performed well until his error made it 1-1.
He did make a crucial save later on to deny Antonee Robinson as the game ended in a draw.