After a goalless first half, it took just three minutes of the second half for the Reds to score.
Oteh, on his away debut, scored after solo effort, blasting forward and weaving through, two defenders before slamming past Mark Oxley into the bottom-left corner.
But 14 minutes later Brahima Diarra, who had been a real handful all night, equalised. But Reds fought back and Tsaroulla scored with 11 minutes to go.
And they were given some breathing room by the in-form Tom Nichols, who scored in the 84th minute.
John Yems made two changes to the side which drew 2-2 with Stevenage on Saturday with George Francomb and Will Ferry replacing Ludwig Francillette and James Tilley.
Crawley started the first half brightly and were the aggressors in the early stages and they had two great chances within two minutes as Ferry forced a good save from Oxley and Jordan Tunnicliffe headed against the bar from Jack Powell's whipped corner.
Both Tsaroulla and Isaac Hutchinson received yellow cards for late challenges.
Reds were applying waves of attacking pressure towards the end of the first with the main threats being Ferry and Nichols, who have both had efforts blocked.
Tilley replaced Hutchinson at half-time.
And just after Oteh scored, he was replaced by Ashley Nadesan before Diarra equalised. But Reds regained the lead in the 79th minute through Tsaroulla and then extended it through Tom Nichols with six minutes to go. The club tweeted: "Nichols adds another with an outrageous curled effort that goes in off the post from outside the area."