Jerome was controversially sent off as Stoke consolidated their position at the top of Group E.
It seemed little could go wrong for the Potters after first-half headers from Kenwyne Jones and Jerome and a finish from Shotton had put them firmly in the driving seat.
They were then reduced to 10 men as Jerome collected a second yellow card in the 43rd minute having been – somewhat harshly – adjudged to have elbowed Yoav Ziv, but the Maccabi player was shown red in a bizarre incident early in the second half and the hosts had little trouble seeing out the victory from there.
Stoke now have seven points from three games at the midway point of the group stage and look well on course to make the knockout rounds.
Potters boss Tony Pulis made seven changes to his first XI, with Matthew Etherington, Marc Wilson, Matthew Upson and captain Ryan Shawcross the only survivors from Saturday’s Premier League victory over Fulham.
Jones, who was making his first appearance since picking up a hamstring injury a month ago, Jerome and Robert Huth were among those coming into the team, while Peter Crouch and Jon Walters were named as substitutes.
After the Israeli visitors had made an assured-looking start, Stoke almost took the lead in the 11th minute when Jerome headed Shotton’s long throw against the bar and saw Maccabi goalkeeper Guy Haimov push away his follow-up.
Within seconds of firing that warning, the Potters made the breakthrough, Jones rising unmarked in the box to crash home Dean Whitehead’s corner.
Wilson sent a chip into Haimov’s arms and Jerome glanced Huth’s cross wide.
The hosts then made it 2-0 from another set-piece, Etherington curling in a free-kick from the right in the 24th minute and Jerome nodding the ball in.
Maccabi attempted to muster a response and Upson got across to block a shot from Moussa Konate, but Stoke were soon back on the attack and extended their advantage just after the half-hour mark.
Jerome found himself through one-on-one with Haimov and took the ball around the onrushing goalkeeper before squaring to Shotton, who converted neatly.
The Potters’ momentum showed little sign of letting up, with Jones bouncing another header into Haimov’s body and Jerome lifting an effort over the bar from Shotton’s cross.
The first half ended on a sour note for the home side, though, as Jerome – who had earlier been booked for dissent – was shown a second yellow card when Greek referee Anastasios Kakos ruled that he had caught Ziv with his arm, a decision which left Pulis incensed.
The Stoke supporters also made their unhappiness clear, booing Ziv every time he touched the ball having felt his reaction to Jerome’s contact had been overly dramatic.
So it was to the great delight of the home crowd when Ziv was dismissed himself in comical fashion 10 minutes after the restart.
Frustrated that no free-kick had been awarded when he was tackled by Shotton by the touchline, Ziv kicked out and managed to fire his boot – which had come loose in the challenge – flying into the assistant referee. His immediate apologies were to no avail and he received a straight red card.
Once the commotion had subsided, Jones almost netted his second of the evening with a header from Shotton’s cross that went inches wide.
At the other end, Konate sent a shot off-target before Pulis threw on Walters and Wilson Palacios for Huth and Etherington.
Soon after, Palacios fed Jones, who drew a good save out of Haimov.
Another Potters substitute, Andy Wilkinson, fired an attempt wide in stoppage time but Stoke’s work was done.