Defeat was Chelsea's second successive home loss and came after it looked as if they had secured a point when Daniel Sturridge cancelled out Maxi Rodriguez's first half opener with an equaliser ten minutes after the restart.
But Johnson's late strike ensured his former club suffered a third defeat in four Premier League games and moved Liverpool up to sixth, level on points with the Blues.
Chelsea's recent dip in form has provoked questions about Villas-Boas's long term prospects at Stamford Bridge and the sound of his side leaving the pitch to boos will do nothing to strengthen his position.
Villas-Boas sprang a surprise before kick-off, omitting Fernando Torres from his starting line-up, denying the striker the chance to face the club he left for £50 million during last January's transfer window.
Liverpool manager Kenny Dalglish mirrored his opposite number's move by leaving Andy Carroll, Torres's £35 million replacement, on the bench.
But it was Dalglish who had more cause to be satisfied during a first half when the defensive lapses that had marred Chelsea's last home outing, the 5-3 defeat by Arsenal, resurfaced with alarming regularity.
Liverpool, who were wearing black armbands following the death of Luca Jones, the five-year-old son of reserve keeper Brad Jones, 48 hours previously, were impressive from the start.
While the visitors chased and harried, Chelsea were surprisingly lethargic and repeatedly conceded possession in dangerous areas far too frequently.
A 22nd minute Didier Drogba free kick almost gave the home side the lead but it was Liverpool who were in the ascendancy with striker Luis Suarez apparently unaffected at facing an FA charge following allegations he racially abused Manchester United's Patrice Evra.
Both Suarez and Chelsea's John Terry, accused of racially abusing QPR defender Anton Ferdinand, wore 'Kick it Out' T-shirts during the warm-up, as did their team-mates with Sunday's match being dedicated in support of the anti-racism campaign.
The pace of Suarez and Craig Bellamy caused Chelsea's ponderous defence repeated problems and it was no surprise that Liverpool 33rd minute opening goal came from a home mistake.
John Obi Mikel was caught in possession by Charlie Adam as he collected a ball from keeper Petr Cech and Bellamy took up the baton, exchanging passes with Suarez before picking out Rodriguez who finished right footed.
Chelsea didn't learn from the error and they were fortunate to avoid falling two behind before half time when David Luiz was caught in possession on the edge of his own area.
The pressure was on Villas-Boas to act decisively and to the manager's credit, he withdrew Mikel at half time, introducing Sturridge.
Chelsea didn't have to wait long for the equaliser, however, with Florent Malouda carving out the 55th minute opening with a powerful run and cross from the left that Sturridge turned home from close range at the far post.
Moments later Chelsea almost took the lead when Branislav Ivanovic's header was superbly saved by Pepe Reina.
Torres and Raul Meireles, another former Liverpool player, were finally introduced in the 84th minute but the decisive late act came from Johnson who collected Charlie Adam's crossfield pass, cut into the box from the right and slotted the ball home left footed.
Source: AFP