The rarely-used striker was thrust into the fray in the second period and provided the crucial touch in the 87th minute to turn the ball beyond Salvatore Sirigu to complete the 2-0 victory needed to take his side through.
Fellow substitute Andre Schurrle had put the clash back in the balance with his opener in the 32nd minute, but it was Ba's most memorable moment for the Blues which had Jose Mourinho haring down the touchline to celebrate with his players by the corner flag.
Mourinho had gambled on the fitness of Samuel Eto'o, including the striker in his starting XI after missing three games with a hamstring injury.
There were no signs of rustiness from the forward as he saw a shot from Eden Hazard's excellent low cross deflected behind for a corner, before swiftly closing down Sirigu after a loose touch, only to be too eager and concede a foul on the goalkeeper.
The Blues suffered a significant blow in the 18th minute with Hazard limping out of the action and Schurrle slotting into the wide attacking role vacated by the Belgium international.
Sirigu was called into action again in the 28th minute, fisting the ball behind after plunging across his goal when Frank Lampard's free-kick from the corner of the box, awarded for Marco Verratti's pull-back on Oscar, took a wicked deflection off the wall.
But the breakthrough came on 32 minutes when a routine throw from the right flank was flicked on by David Luiz with substitute Schurrle allowed to ghost in unchecked and side-foot home from 12 yards out to spark scenes of jubilation at Stamford Bridge.
There were half-hearted appeals for a penalty soon after as Schurrle collided with Verratti in the box, but referee Pedro Proenca was unimpressed, with PSG breaking down the field and Lucas hammering a shot way over the bar.
Gary Cahill had a glorious opportunity to grab the second for Chelsea before the break, but snatched at the chance in the area after Lampard's free-kick deflected up into the air off Edinson Cavani's shoulder and only found the fans behind Sirigu's goal.
Lucas threw himself to the ground over John Terry's outstretched leg on the edge of the Chelsea box early in the second half, but again referee Proenca waved play on and elected to take no action against the PSG player.
PSG's goal then lived a charmed life as Chelsea struck the face of the crossbar twice in as many minutes, with Schurrle's first-time effort after a neat move the first to rattle the frame, before Oscar's dipping free-kick also beat Sirigu but not the woodwork.
Petr Cech had to be alert to palm away Ezequiel Lavezzi's whipped free-kick towards the far post in the 57th minute after Branislav Ivanovic's foul on Blaise Matuidi, with the defender receiving a booking to rule him out of the semi-final first leg.
Mourinho sent on Ba in place of Lampard with 66 minutes gone, with the striker soon in the action to flick on towards Schurrle, but the German's shot took a deflection on the way through to Sirigu and was easily gathered.
Cavani fired a dipping effort narrowly over Cech's bar in the72nd minute and Maxwell was only just off target after Chelsea were sloppy in possession in the middle of the park as a few gaps began to appear with the Blues pushing forward.
Former Newcastle man Yohan Cabaye then played in Cavani with an excellent through-ball, but the striker again failed to test Cech with PSG's best chance of the night.
Mourinho threw on Fernando Torres for the final 10 minutes and the breakthrough came with just three minutes remaining when Ba was on hand to scoop home from six yards out after a deflected shot from the edge of the box, before Cech made a crucial stop from Marquinhos deep into added time.