Peschisolido was undoubtedly the difference between the sides as, apart from his 61st-minute winner, he could have set up three other goals but was badly let down by his team-mates' finishing.
It was his ninth goal of the season which mattered most as the home side found the net after a five-and-half-hour barren spell which had contributed to them losing their last three First Division matches.
It was far from comfortable, though, for last season's beaten semi-finalists as Colchester went close to earning a replay and with it another shot at reaching the sixth round for only the second time in their existence.
But Peschisolido was the thorn in their side from early on and provided gilt-edged chances for Wayne Allison and Phil Jagielka inside the opening 22 minutes.
The Canadian striker first dispossessed Liam Chilvers in the 13th minute before teeing up an all-alone Allison, who stabbed wide, and nine minutes later Jagielka sliced wide after accepting Peschisolido's lay-off.
It was not all one way, however, as Paul Tierney and Kem Izzet set up Wayne Andrews for a crisp 20-yard drive which Paddy Kenny superbly clutched on the line.
Kenny was again called upon in the 28th minute, just nudging wide a 25-yard free-kick from captain Karl Duguid after Peter Ndlovu had become the first player booked for a foul on Joe Keith.
If Warnock had been hoping for a change of fortune after the break, it failed to materialise within the opening two minutes of the second half as another two chances went begging.
After 25 seconds Allison fed full debutant Dries Boussatta inside the area, but a stabbed shot from 12 yards was narrowly wide, before Ndlovu then teed up Peschisolido, only for Alan White to block.
The visitors were not rattled, and four minutes later should have taken the lead when Duguid pounced on an Alan Wright mistake before releasing Rowan Vine. He should have taken Duguid's pass first time, but instead an extra touch allowed skipper Rob Page to throw himself in front of the eventual drive.
Warnock's men looked as if they were running out of options until finally making the breakthrough just after the hour, and deservedly through Peschisolido.
Wright atoned for his earlier error by whipping a free-kick from the right into the near post where Peschisolido arrived to power a header past Simon Brown and become his side's leading scorer this season.
Ndlovu should have killed the tie four minutes later but, after cutting inside Sam Stockley, his fierce shot was brilliantly pushed away by White.
After Izzet had curled a 30-yarder inches wide, Peschisolido set up 78th-minute substitute Andy Parkinson - recalled from a loan with Notts County and who played 90 minutes in Saturday's 1-0 defeat at Bournemouth - only for Stockley to keep him at bay.