The burly frontman from Hull City struck his first goal in his temporary club's colours in the 78th minute before Rolando Aarons looked to have dragged the tie into extra-time with an 88th minute equaliser for Newcastle United.
However, with an additional 30 minutes looming, Mclean beat the offside trap to coolly fire home and ensure Richard Beale's development side will be waiting to find out their opposition in the next round at midday tomorrow (Wednesday).
As well as Mclean, Beale was also able to start another player fresh from their first-team debut against Blackpool on Saturday
, midfielder Dariusz Dudka, while Demarai Gray missed out through illness.
It was until after the break when this round of 32 tie truly came to life but Blues had edged what few chances arrived in the first-half. Dudka forced Jak Alnwick into a fine save with a dipping effort from 12 yards in the 12th minute while the Magpies goalkeeper was almost caught off guard moments later when trialist Brendan Daniels' cross from the right wasn't dealt with.
Charlee Adams, operating as a makeshift centre-back, had the best chance of the first-half and it came on the stroke of the break. Reece Brown's corner from the left was half-cleared to Adams on the edge of the area and his thunderbolt was brilliantly tipped away by Alnwick.
Newcastle's Brandon Miele set the tone for a lively second-half when, 30 seconds after the restart, his saw his low drive from just inside the area scooped up by Colin Doyle. The visitors continued to come on strong and Harris Vuckic bent a decent effort wide of the mark from the right side of the area in the 55th minute.
At the opposite end in the 68th minute, Olly Lee's powerfully struck left-footed effort from distance looked destined for the corner of the net but sailed inches wide.
Then came Mclean and Blues' opener, arguably the finest strike of the match. The 30-year-old pounced on a long ball down the right, rolled his marker and powered an excellent effort into the far corner. Mclean could have even bagged a second in as many minutes when he again got the better of the Geordie backline to beat the onrushing Alnwick but not the crossbar.
When Doyle did well to beat away Aarons' effort in the 85th minute, it looked as though Newcastle's chances had gone. However, with two minutes of normal time remaining, Aarons latched on to a diagonal ball on the right side of the area and slid his shot underneath Doyle.
As those inside St. Andrew's braced themselves for an extended afternoon of action, Mclean raced on to Adams' header from the back to calmly slot a low effort beyond Alnwick.
Blues U21s: Doyle (C); Higgins, Adams, Kelly, Moseley; Daniels (trialist) (Webb 83), Dudka, Lee, Solomon-Otabor (Arthur 62); Brown; Mclean.
Subs not used: Preston, Hales, Truslove.
Newcastle United U21s: Alnwick, Tavernier, Haidara (Morgan 76), Bigirimana, Satka, Gillesphy, Aarons, Miele, Campbell, Vuckic, Sammy Ameobi.
Subs not used: Mitchell, Olley, Quinn.