Yes, since the damage halvings come from two stackable game features.
Resistance is applied after the modifiers of the damage, see the basic rules:
Resistance and then vulnerability are applied after all other modifiers to damage.
The first modification is the halving thanks to the successful saving throw, then the barbarian halves the remaining damage due to their resistance. The above rule tells how to deal with game features that modify the incoming damage: first of all one has to consider all the bonuses/maluses, flat reductions, halving coming from class features (such as Uncanny Dodge), and then apply resistance (or vulnerability).
If the barbarian had a further resistance to bludgeoning/slashing/piercing damage, provided for example from a Warding Bond spell cast by the party's Cleric, this latter resistance would not stack with the one given by the rage. This rule can be found again here:
Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance. For example, if a creature has resistance to fire damage as well as resistance to all nonmagical damage, the damage of a nonmagical fire is reduced by half against the creature, not reduced by three-quarters.
This is confirmed by the Sage Advice CompendiumSage Advice Compendium too:
A dragon uses a breath weapon against me. I succeed on the save, and I have resistance to the damage. Do I take only one-quarter of the damage? Yes, because resistance is applied after all other modifiers to damage (PH, 197). If you succeed on a save and still take damage, that damage is halved if you have the right resistance.
The monster and the type of the damage are different, but the reasoning is the same.