Everton leave it late to secure Martínez his first win and a third round clash away to Fulham.
Deulofeou looked equally impressive as he skinned Shroot and put it on plate at the back post for Koné who could not convert from a yard out. Deulofeu continued to torment stand in left back Roarie Deacon as he put a number of great crosses in, but Everton were not switched on in the final third.
We continued to dominate the game but we were still looking for that elusive first goal. Deulofeu came close as he curled a strike from the edge of the box just wide.
It was then in typical fashion that we conceded. A long ball from Deacon met Tounkara who had time to cross it into the area. Our back line ran around like headless chickens as Smith scuffed a shot before the ball fell to Freeman who rifled it into the net.
We looked to be heading into half time a goal down as Koné missed another chance from 8 yards out, but Deulofeu managed to pull 1 back as he drove forward, turned 2 defenders and buried a left footed shot into the far corner.
Everton continued to create chances in the second half, but the tempo dropped as the game went on. Stevenage managed to force extra time and given our luck in the League Cup, I was beginning to think the worst.
Fellaini was introduced for Barkley and came close to scoring twice as penalties loomed.
Then following some awful defending from Stevenage, the ball fell to Fellaini in the box who put his foot through it to send the Blues into the third round.
Full time. Everton 2-1 Stevenage.