James' finish capped a fine Blues victory, with the England wing-back also teeing up Pierre-Emerick Aubameyang for his second goal in as many games.
Wesley Fofana opened the scoring, tapping home after Thiago Silva's powerful header, only to hobble out in the first half with a potential leg injury.
Chelsea leapfrogged Milan into second place in Group E on goal difference by registering their first win in their third Champions League encounter this term.
New manager Potter might have got off the mark on the win front in Saturday's 2-1 Premier League win at Crystal Palace but the former Brighton boss was still hunting a landmark performance and result to stamp his authority on Stamford Bridge proceedings.
And when James rifled home the third goal, that ultimate aim of quality amid victory was fully assured.
Potter's first Blues outing ended in a mixed 1-1 Champions League draw with RB Salzburg on September 14 but already the Solihull-born coach's methods look to be bearing fruit.
Mason Mount's low strike forced a solid save from Ciprian Tatarusanu to open the night.
Chelsea's major early threat came from set-pieces, and Silva powered in two headers that proved important range-finders against his former club.
The ageless Brazil centre-back then thundered in a third header, forcing a parry from Tatarusanu and leaving Fofana to sweep Chelsea into the lead.
Mount chipped home to cap a fine move after Aubameyang's dinked pass, only for the effort to be chalked off for offside.
Fikayo Tomori was booked for dissent on his Stamford Bridge return, the ex-Chelsea defender right in the midst of a gripping and tetchy encounter.
Goalscorer Fofana then hobbled out of the night with that injury concern, with Trevoh Chalobah thrust into the fray.
The hosts dominated the half but almost fell prey to a last-minute sucker punch.
Long-term Blues target Rafael Leao jinked into the box and fired in a low shot that Kepa could only parry back into the danger area. Rade Krunic raced on and let fly, only for Ben Chilwell to produce a vital block to deny what would surely otherwise have been a Milan equaliser.
Aubameyang quickly doubled Chelsea's lead in the second half, applying a facile finish to James' cross.
Milan's defending doubtless left much to be desired, but Chelsea cannot overvalue the presence of a central striker lurking in front of goal.
Romelu Lukaku struggled last term in not only finding such threatening central positions but also receiving the requisite service to deliver the goal demand.
Aubameyang's two goals in consecutive appearances both fit the clinical bill, and all in west London will hope this return proves merely the start.
Chelsea refused to sit back and admire their situation, with the hosts seemingly aware of the need for a statement to rubber-stamp Potter's arrival.
James' finish quickly sealed that deal, and in some style. The marauding wing-back powered into the box and unleashed an unstoppable, rising effort that flew in at the near post.