Berrettini beat tournament favourite, Cameron Norrie, in the final as Humbert beat Andrey Rublev in Halle.
The Swiss maestro won the opening set but failed to build on that momentum as he lost the remaining two sets to bow out of the tournament.
Nadal's fourth-round opponent will be Jannik Sinner in a match definitely promises to be an enthralling encounter.
In a lopsided final, the Greek sensation defeated the British player in straight sets in the final on Sunday.
The Austrian player suffered a shock 6-3, 6-2 defeat against Cameron Norrie at Lyon Open on Thursday.
Elsewhere, Cameron Norrie downs Marin Cilic in a tight contest to enter Estoril final.
Meanwhile, Wesley Koolhof and Kevin Krawietz advanced to the BMW Open final in Munich.
The Spaniard, who also needed three sets in his previous round, will next play Cameron Norrie in Barcelona