Both sides came into this game on the back of an opening day league win as attention turned to the first&nbsp;cup competition of the season.&nbsp;
Palace manager George Burley's team selection was hit by injury, suspension and also Owen Garvan being away on international duty. 19 year old Nathaniel Pinney started the game in one of three changes from&nbsp;that win on day one.
The visitors had the first chance on goal when Pinney picked up a loose ball just outside the box on four minutes but his fierce shot was turned over the bar by goalkeeper John Sullivan. Just a couple of minutes later he was in again but his shot was blocked by the 'keeper.
It was his strike partner, Andrew, who had the next chance when his header was pushed away by Sullivan as the league one side were put under some early pressure.
The home side replied at the other end but were denied by the woodwork. Luke Freeman, on loan from Arsenal, saw his&nbsp;shot hit the&nbsp;bar after he collected a cross by Nathan Jones&nbsp;and the dangerous loose ball was cleared by the defence.
Town were in again when Dean Bowditch received a through ball just inside the box but he turned the ball over the bar with Julian Speroni to beat.
After a quiet spell in the game there was then chances at both ends as an outswinging corner fell to Andrew Williams who played the ball back across goal with Speroni already committed but Paddy McCarthy was there to get the ball under control and clear upfield.
Two chances then at the other end for Alan Lee. Firstly he was beaten to the ball by Sullivan as he chased towards goal but then he was on hand to meet a Julian Bennett cross into the box but Lee saw his header go just wide of the target.
Both sides went into the break all square but if it wasn't for their goalkeeper the home side could have been out of the tie in the opening stages&nbsp;but as the half progressed the league one side came more into the match.
One change made at the break by Burley as Wilfried Zaha replaced Pinney.
Palace thought they had taken the lead early in the half as the ball was played through to Darren Ambrose who made no mistake firing past Sullivan but the official disallowed the chance as he adjudged the scorer was in an offside position.
On 56 minutes Julian Speroni kept his side on level terms with a fine save from a free kick just outside the box. A challenge on Sam Williams had given Town a free kick and a powerful shot by Bowditch was punched away by the 'keeper.
A further substitution was made from the bench as Kieran Djilali replaced Andrew just before the hour mark.
Zaha nearly added to his opening day effort when he was on hand to meet a cross from Nathaniel Clyne but his diving headed chance went just over Sullivan's goal.
As the game entered the final twenty minutes the visitors enjoyed some good possession and won a couple of consecutive corners. From the second one Ambrose found the head of Adam Barrett but the chance didn't trouble Sullivan as it went over the target.
The home support were left frustrated when they thought referee Phil Gibbs should have awarded a spot kick when Bowditch went down in the box under a challenge but the appeals were waved away by the official.
At the other end, with eight minutes remaining, Cadogan showed his pace down the right after being put away by Ambrose and after making his way into the box saw his shot curl away from goal as he made the strike.
As added time was signalled by the 4th official came the deciding goal of the evening came about. A cross from the left by Djilali was spilled by the keeper and then it fell to Cadogan whose shot was blocked and but&nbsp;Lee made no mistake for his second goal in two games to give Palace the late advantage.
That was to be the last chance for either side&nbsp;as the visitors&nbsp;progressed through to round&nbsp;two courtesy of the added time close range effort&nbsp;by Lee to put out the league one side. &nbsp;
Yeovil Sullivan, Alcock, Huntington, Virgo, Jones, Andrew Williams, Ayling, Kalala, Freeman (Smith 73),Sam Williams, Bowditch.
Subs Not Used: Roberts, Stam, Hutchins, Upson, Calver, Matthews.
Crystal Palace Speroni, Bennett, Barrett, McCarthy, Clyne,Cadogan, Ambrose, Dorman, Andrew (Djilali 58), Lee,Pinney (Zaha 46).
Subs Not Used: Price, Davis, Holness, Holland, N'Diaye.
Att: 3,720&nbsp; Referee: Phil Gibbs (West Midlands).