Zeus most glorious and most great, Thundercloud, throned in the heavens! Let not the sun go down and the darkness come, until I cast down headlong the citadel of Priam in flames, and burn his gates with blazing fire, and tear to rags the shirt upon Hectors breast! May many of his men fall about him prone in the dust and bite the earth!
-Homer
Campaigns against the Sabines
A history of Rome, by Prof Alfred Kennard, 2002 New York
In 332 BC it came to the first battle of the war. The Umbrian League was not trying to confront the Roman army directly rather then try to bleed and starve the Roman people into submission. But when the Romans made Quintus Camillus Furius dictator they choose a relatively competent man to deal with the problem. He quickly gathered all men at the Fields of Mars and marched against Cures, where the Sabines met the Romans for battle. The Sabines used a mixed of older tactics like chariots but also used heavy infantry not unlike the Romans.

Roman infantry facing chariots.
The odds were even, but if we are to believe Fabius the Roman army was better supplied and the moral of the men was at a peak. The Sabines tried to break the roman wedge formation by two attacks, but Furius broke through the enemy at the spearhead and broke the army into two. Panic spread and the whole Sabine army routed from the field. Fabius tells us that the Romans had only a couple twenty Roman casualties. While this is certainly an exaggeration it is not unlikely that the Romans won an overwhelming victory over the Sabines. It is also possible that Fabius wanted to underline that competence of Furius as a competent commander, who was not appointed in any significant military position the next years, even though we have no clue why he didn't get any further command.

The battle was a surprising loss for the Umbrian League and for the next 3 years both sides would not engage each other in a larger battle. The Romans would build up fortified colonies in Latinum with the task of defending the lands while the Umbrian League tried to drag the Samnites, probably the strongest rival to Rome, to join the Umbrian League.
Fabius - Ab Urbe Condita
(written at about 50 BC)
Book VIII
(18) When a Umbrian messenger arrived at Kelis Puntiis who was at that time elected meddix, a position that resembles our consul, he offered him to join the Umbrian League as a coequal ally to get revenge at the Romans from the last war with them. Kelis Puntiis replied: "What a tempting offer. But how do I know that you Umbrians do have what it takes to fight the Romans, when you have troubles of keeping the Umbrian League together?" The messenger replied: "The Umbrians lead the league, it was written in stone when we formed our band, now the other members of the league want the lead for them. The Umbrians do honour their agreements for good or evil, therefore we will not give up leading the league. But the Samnites would join as ally with equal vote and rights. Without having to bother with the other members at all." Puntiis thought about it and answered: "Your ideas and goals are just. But I don't believe that the league can survive and function with such quarrel within the own ranks. The Samnites will join the war, but not as ally. Instead we will join as comrades in arms." And so it happened that the Romans now fought the Umbrian League to the north, and the Samnites in the south.
Cont. A history of Rome
We do not know the exact year when the (second) Samnite war started along the war with the Umbrian League, but most historians agree with the year 329 BC.
From 331 BC to 328 BC the Romans fought the Umbrians and the Etruscans with mixed results. There was no clear advantage on both sides. In 328 BC Spurius Aemilius Mamercus and Publius Cornelius Scapula were elected consuls. Fabius tells us that it was Mamercus who favoured a new decisive attack on the Sabines to knock them out of the war since the various smaller battles and skirmishes against the Etruscans and the Umbrians were not leading anywhere. This was a tricky plan since moving the Roman legions into the Apennine mountains, the heartland of the Sabines was a dangerous move that would expose the Roman flanks and make it possible for the Umbrian allies to attack Rome directly. But Mamercus took the risk and attacked Sabine homeland and forced them to face them in battle.
(21) Since the Romans were invading their own land the commander of the Sabines had, Magistrate Aninis had the choice of battle. He knew that the Roman army was terribly mobile so he placed his army at a hill, hoping to slow their movements. Mamercus scouted the area and placed his heavy cavalierly near a local wood within the hill. That way Aninis thought that the Romans would attack without the crucial flanking force. When all the Hastati engaged the Sabine lines a horn was blown and the Equites started moving up the hill out of sight and flanked the Sabines on the left wing, crushing through the main line of defence. The terror of the Roman Equites breaking out of nowhere surprised the Sabines who were struck by shock and started fleeing from the battlefield. The Romans finished off the complete army killing thousands of Sabines, even though the attack on the hill itself cost the Roman many fine Romans their life as well.

Roman infantry engaging the Sabine line of defence.

The Sabines had a tight line of defence that could not be broken through with normal infantry.

The Roman Equites charged into the back of the infantry line and breaking through the ranks.
(22) When Magistrate Aninis returned to Carseoli [the capital], for he had survived the battle, he ran into the Senate and cried: “All is over! All is over!”. When the Sabine senators asked Aninis to calm down he explained that they lost the war, for the whole army was lost itself and the Roman consul was on the way to the city. So the Sabine Senators all agreed that the war was over and it was time to surrender to Roman mercy. For his great deeds Mamercus was granted a triumph upon returning home with his successful army.
The 6 areas at the bottom of the trapeze mark the landgain made against the war with the Sabines.
Mamercus battle against Aninis was fought at an unknown location in the year 328 BC and it was the second great victory over the Sabines, who had not achieved any victory themselves against the Romans. The Umbrian League was breaking up the moment the Sabines decided to make peace with the Romans. In fact the Romans acquired nearly all Sabine territory except some Sabine colonies on the eastern coast of Italy.
Rome had defeated the weakest enemy, which was important enough to weaken the Umbrian League to a great deal itself. Now the focus was on a war on two fronts, the Umbrians and the Etruscan to the north and the Samnites to the south. Rome was still much on the defence and facing superior number of troops. Furthermore, not every campaign would go as smooth as the ones against the Sabines as the next battles would show.