Dulwich were quickly into their stride, forcing Harrow to defend for long periods. Ashley Carew had a goalbound shot blocked and Terrell Forbes just failed to get on the end of a Kershaney Samuels chip to the far post.
There was one scare as Oshane Brown was penalised for holding on to the ball too long but the free kick was blocked before being cleared to safety.
The opening goal came on 19 minutes after a fine move from deep in the Dulwich half. Nyren Clunis was sent away on the right and his cross found Ashley Carew whose effort brought a fine save from Jupp in the home goal. It was Carew who took the resulting corner which fell to debutant Jack Dixon on the edge of the penalty area. He fired a first time shot that beat the Jupp low to his right.
Nyren Clunis headed just over and Omar Koroma had an effort saved as Dulwich remained in the ascendancy. With half time looming Koroma showed great footwork to get clear on the right but his cross flashed across the six yard box.
In added time at the end of the half, Brown had to be smartly off his line to block after a through ball sent a Harrow forward in on goal.
Half Time 0-1
Dulwich were soon on the attack again at the start of the second half and a 48th minute cross from Frazer Shaw was headed just over by Omar Koroma. Oshane Brown produced a good save three minutes later as he held a deflected shot as the home side pushed forward.
On 56 minutes Dulwich doubled their lead. Nyren Clunis had a shot well saved by Jupp and after he cleared the ball, a defensive splitting pass from Ashley Carew set Clunis in on goal. He beat Jupp and as a defender tried to clear off the line managed to force the loose ball home.
Dulwich were now pressing the home side back with neat passing that saw them switch the attack from side to side across the pitch. One such attack saw Carew find Koroma who quickly moved the ball left for Frazer Shaw whose shot was deflected wide.
Just past the hour mark, Xavier Vidal was just wide with a rasping shot that had Jupp beaten and Kershaney Samuels was just too high with a 64th minute effort after good work on the right from Carew and Vidal.
Three minutes later had an effort well held by Jupp before the third goal arrived in the 71st minute. Ashley Carew's corner saw Terrell Forbes shot blocked, Jack Dixon's follow up was well saved by Jupp but Omar Koroma forced the ball home.
This was the last action for Koroma who was replaced by Harry Ottaway for his first serious action of the season.
Clunis had a good chance to make it four with ten minutes left but he failed to get any elevation on his chip and instead put the ball in Jupp's grateful hands.
Harrow went straight to the other end where Brown had to pull off a fine diving save, but from the resulting corner Harrow substitute Greg Ngoyi headed home.
Harrow now sensed a way back into the game and exerted some pressure on the Dulwich goal without calling Brown into any more serious action other than to effectively punch clear a couple of good crosses
In fact, with four minutes left, Dulwich passed up a good chance as a square ball across the six yard box saw a limping Nyren Clunis unable to get on the end of it.
Harrow did have one further chance in stoppage time but a rising drive was sent too high.
Final Score 1-3