There's the question if anyone could have really won Investiture Controversy.
Rome didn't had a clear "victory" IOTL, and eventually went trough a compromise or agreement with temporal powers (HRE, but as well other realms).
A total victory would have been out of reach, as asking for the irremediable disappearance of one of the actors, destabilizing enough feudal society to assure huge troubles for the victor.
Now, could HRE have a better deal off the controversy? I think it's possible.
A first possibility would be to get rid of the Controversy as it happened IOTL by a more smooth gregorian reform : having Ottonian dynasty living on, by exemple, could allow a better (if still troubled) relationship between a politically growing papacy and the emperors.
Emperors as Henri III, skilled enough to not have huge revolts and sit on the fence between great lay lords and ecclesiastical power, could allow the situation to decant more or less as IOTL but at the difference emperors would be actor of this change and not accepting it eventually.
If you still want a Controversy as it happened IOTL (as it, after Dictatus Papae) , the best would be that Henri IV imposing a pope after Gregorius' death. It shouldn't be Clementus III that is completly discredited, but someone else elected at this occasion, while the emperor still have a real grasp on Italy.
In order to do that, however, Henry IV should make actual compromise with Italian nobility and clergy. If not this election wouldn't be acknowledged.
Whatever the cause, if it succeed, you'll end probably with an integration of laicisation of ecclesiastical demesnes into imperial administration, rather than being apart.
Immediate consequences wouldn't be that different, but it would certainly prevent the theocratical monarchy conception of papacy to fully appear, and critically prevent later conflicts as during Frederic II's reign.
As for "centralization" of a feudal empire, I'm afraid that's not possible. It's actually a contradiction, feudality being about delegation of property and power.
Now, if you meant "unified" HRE, then it's more probable, but wouldn't be a direct consequences, especially regarding lay lordship that would be relativly untouched institutionally.
Having more close ecclesiastical vassals, on the other hand, could prevent more critical aspect of political crisis.
Rather than allowing more unification, it open possibilities.