Taylor spotted Everton goalkeeper Tim Howard off his line as the ball broke to him after Nwankwo Kanu had tackled Simon Davies.
The former England under-21 defender unleashed an unstoppable lob from the edge of the centre circle that dipped over the helpless Howard and into the net.
Taylor wheeled away to celebrate with a stunned Pompey bench and leapt into the arms of substitute Richard Hughes in delight.
Everton paid the price for a crippling injury list and were without their entire first-choice midfield, with Tim Cahill, Mikael Arteta, Phil Neville and Leon Osman all absent.
It took until the 12th minute for either side to threaten a shot on goal.
Everton defender Alan Stubbs threw himself in the way of Benjani's attempted long-range effort, before captain David Weir blocked Glen Johnson's follow-up.
Taylor had the whole of Fratton Park on their feet with his stunning solo strike in the 14th minute.
Pompey had David James to thank for keeping their lead intact six minutes later when he pulled off a fine one-handed save to deny Joleon Lescott his first Premiership goal.
Stubbs picked out Lescott at the back post with a chipped free-kick and the defender nodded the ball down towards the bottom left-hand corner before James made the stop.
Former Southampton striker James Beattie should have done better when he latched on to Joseph Yobo's 25th minute cross only to head straight at James.
Pompey manager Harry Redknapp could have been forgiven for doing his own victory jog when Kanu doubled Pompey's lead less than a minute later.
The rejuvenated Nigerian guided Gary O'Neil's right-wing centre into the bottom left-hand corner with a perfectly-executed left-foot volley for his ninth of the season.
Benjani could have done with some of Kanu's coolness soon after when he fired hopelessly over from the edge of the penalty area.
Sean Davis attempted to repeat Taylor's heroics when he tried to lob Howard from the edge of the box, but this time the on-loan Manchester United keeper managed to scramble back and keep the ball out.
On a day for the spectacular, Andy van der Meyde put an ambitious 25-yard drive wide of James' left-hand post ten minutes before half-time.
Taylor came close to adding a second with a 20-yard free-kick that sailed just over Howard's crossbar.
Everton boss David Moyes made two changes at the interval, hauling off Beattie and the hapless Weir and replacing them with Victor Anichebe and James McFadden respectively.
Stubbs came close to getting the Toffees back into the game with a well-struck 30-yard free kick just over in the 54th minute.
Benjani should have done better when he raced on to Taylor's flick four minutes later, only to dive over the on-rushing Howard and look for a penalty when all he had to do was flick the ball past the American.
James was sent scrambling across his goal to keep out Yobo's header from van der Meyde's out-swinging cross 16 minutes from time, as Everton produced a more spirited second-half showing.
No comeback was to materialise, however, with substitute striker James Vaughan lucky to escape a red card late on for a last-minute elbow on Sol Campbell.