Pompey dominated the opening half an hour and took the lead through Terry Devlin's long-range screamer.
But Rangers scored three times in 15 minutes before half-time to earn a first win away to Pompey since May 2000.
Portsmouth named £2.5million new-boy Abu Kamara in their starting 11 while QPR handed league debuts to goalkeeper Pierce Charles and Boy Kemper.
Adrian Segecic's early corner was headed wide by Conor Shaughnessy before summer signing Luke Brooke-Smith unleashed a stinging shot from 25 yards straight into the arms of Pierce Charles.
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Rangers' first sight of goal came in the 12th minute when Pompey failed to properly clear a corner and Chair saw his goalbound effort blocked in front of the line by Ebou Adams.
Portsmouth took a deserved lead in the 15th minute when Northern Ireland international Devlin picked out the corner of Charles' net with a stunning 30-yard curler.
Rangers suffered another setback when Kemper was forced off injured with only 20 minutes played.
Portsmouth were inches away from doubling their lead as Kamara was close to getting on the end of Zak Swanson's teasing far post cross.
The home side were clearly enjoying themselves in front of a near 21,000 sellout crowd in the south coast sunshine.
The dangerous Segecic latched on to Colby Bishop's clever flick-on before whipping in a cross that Brooke-Smith could not properly connect with.
Segecic then dragged a shot wide under pressure from Jake Clarke-Salter after being played through on goal by Kamara.
The visitors equalised against the run of play 12 minutes before half-time when Chair was left unmarked to toe-poke home from point-blank range from Harvey Vale's cross.
The home fans were left dumbfounded seven minutes later as Koki Saito's effort from just inside the penalty area took a double deflection off Devlin and Rocco Shein, totally wrong-footing goalkeeper Nicolas Schmid to make it 2-1.
Julien Stephan's men extended their lead in first-half stoppage time when Chair claimed his second with another simple finish from Amadou Mbengue's cross following more awful defending.
Pompey should have reduced the deficit 10 minutes into the second half when Charles passed the ball straight to Kamara but he shot tamely at the keeper with a half-open goal at his mercy.
Man of the match Chair was denied an opening day hat-trick by a smart save with the legs from Schmid at his near post.
Substitute Josh Murphy put a shot into the side netting and two efforts across the face of goal but the hosts never really looked like mounting a comeback.
