The key factor was the Saracens (the Turks, Arabs, etc.) were thoroughly disunited. While the Crusaders had disagreements among themselves, their opponents had even bigger disagreements, and failed to effectively work together.

First, there was a major division of the region between the Seljuq Empire (eastern Anatolia, Syria, Mesopotamian, and Persia) and Fatimid Egypt. Significantly, they fought over the control of Jerusalem, and it changed hands between them, with the Fatimids gaining control during the First Crusade, while the Crusaders were at Antioch. (Following the recovery of Jerusalem from the Crusaders, it reverted to this condition of a front-line city between Egypt and Syria/Mesopotamia; one motivation for giving control of Jerusalem to Frederick II in the 13th century was to have a neutral buffer state between these two warring powers.)

The Seljuqs didn't just face the invasion by the Crusaders, but also a simultaneous invasion by the Fatimids. At least some of them judged the Fatimid invasion to be more dangerous. (The Crusaders negotiated with Fatimid about a possible alliance, but were unwilling to divide Palestine/Syria between themselves and the Fatimids (which would have left Jerusalem in Fatimid hands), and both parties invaded simultaneously but independently.)

Second, the Seljuq Empire had splintered. Anatolia and Syria had been divided between brothers not friendly to each other, and when the ruler of Syria died, control was further divided between his sons, who were even less friendly with each other, the enmity between the emirs of Aleppo and Damascus seriously hampered attempts to fight the Crusaders.

As a result of this disunity, the Crusaders faced only opposition from Kilij Arslan in Anatolia, and he was unable to gather a strong enough force to stop the Crusaders. He resorted to scorch earth methods, which harmed but did not stop the Crusaders, and also attempted to destroy part of the Crusader army at Dorylaeum (1097), after the Crusader army had divided so as to march more easily. Unfortunately for Kilij Arslan, he chose to fight at the place where the Crusader armies had planned to meet again, and the other half of the Crusader army arrived, putting a quick end to the battle.

The early attempts by the Saracens to relieve Antioch failed because they were made in far insufficient force. They were made in far insufficient force because the emirs of Aleppo and Damascus refused to work together (one inadequate attempt by each). After this, an army of sufficient size was gathered, under the control of Kerbogha, Atabeg (Governor) of Mosul. This included contingents from as far away as Baghdad and Persia, and the forces of the feuding emirs of Aleppo and Damascus (and the feuding emirs of Homs and Manbij, and there were disputes between the Bedouin and the Turks from Mesopotamia). On the way to Antioch, Kerbogha spent three weeks attempting to take Edessa (unsuccessfully), to avoid leaving a strong enemy fortress threatening his lines of communication. Due to this delay, Antioch (except for the citadel) fell shortly before his arrival. This left the Crusaders better positioned to face him, with the former garrison of Antioch largely massacred and unable to attack the Crusaders from the rear.

Thus, the second siege of Antioch began. Faced by a choice between starvation, surrender, and fighting Kerbogha, the Crusaders opted to fight. The disintegration of Kerbogha's army began with the desertion from the battle of Duqaq, the emir of Damascus (the "official" reason was that he withdrew in order to fight the Fatimid invasion, but there were accusations that he didn't want Kerbogha's power and influence strengthened by a major victory). Other emirs followed, and Kerbogha's own forces and those of the few loyal emirs who remained were insufficient to defeat the Crusaders.

After recovery from the trauma of Antioch, the Crusaders proceeded to Jerusalem. The local rulers did not combine to offer effective resistance. Some even guided the Crusaders past ambushes attempted by other local rulers (if the Crusaders swiftly passed through their territory, they would become somebody else's problem). Thus, the Crusaders arrived at Jerusalem - compared to their passage through Anatolia, short of food and water courtesy of Kilij Arslan's efforts, and their difficulty at Antioch, their march from Antioch to Jerusalem was a safe journey. At Jerusalem, their main concern was to capture the city before the Fatimids could send an army to relieve the city. The Crusader army was strong enough to take the city by assault, and did not need to resort to an extended siege, and Jerusalem was captured by assault. The incoming Fatimid army was defeated at Ascalon 1 month after the fall of Jerusalem.

The local rulers between Antioch and Jerusalem had little motivation to stop the Crusaders. If they had fought, and especially if they had worked together and fought, they would have slowed the Crusaders. But this would have simply invited destruction upon themselves, and letting the Crusaders pass through in peace to where they might trouble their local rivals, or fight the Fatimids - the recent invader - for control of Jerusalem was a better option in their eyes. The lack of local interest in stopping the Crusaders from capturing Jerusalem from the Fatimids meant that the relief army had to come from Egypt. This easily gave the Crusaders enough time to take the city (with a month to spare).

Antioch (and earlier, perhaps the battle at Dorylaeum when Kilij Arslan caught half of the Crusader army) was a close-run thing, and perhaps there was an element of luck. However, the key factor was Saracen disunity, to the point of much of Kerbogha's army deserting mid-battle. From Antioch to Jerusalem, it was again Saracen disunity that resulted in little opposition. The arrival of wood at Jerusalem should not be seen as a stroke of luck, just as poorly-managed logistics barely managing to perform. it was Seljuq-Fatimid rivalry that had left the path to Jerusalem open, and the city weak enough, with relief forces far enough way, to allow its capture.