The strike partners were at their brilliant best at the Parc des Princes on Tuesday, Cavani netting either side of a superb Ibrahimovic volley to boost PSG's hopes of winning UEFA Champions League Group F
Their efforts, which sandwiched a Davy Klaassen leveller midway through the second period, ensured the French side remained at the summit of the pool - one point ahead of final opponents Barcelona.
Few gave the visitors a chance heading into the clash, with PSG battling with Barca to reach the last 16 as group winners having already sealed their progression.
And Ajax's hopes were further undermined when Cavani grabbed his 10th goal of the season, only for Klaassen to impressively level midway through the second period.
But his fine header merely reawakened PSG, who took their points haul to 13 from five games thanks to their dynamic duo up front.
PSG made a promising start and Javier Pastore launched a counter-attack that ended with Cavani seeing his effort blocked by Mike van der Hoorn.
The home side continued to enjoy the better of the early exchanges as Ajax, forced to withdraw Nicolai Boilesen after 10 minutes due to a knee injury, struggled for a foothold.
Ibrahimovic and Cavani were unsurprisingly the biggest threat, epitomised by the former curling just over from distance.
The best chance in the opening 25 minutes fell to Ezequiel Lavezzi, only for the attacking midfielder to hit straight at Jasper Cillessen after running on to Ibrahimovic's fine throughball.
But the Argentinian was more clinical when Ibrahimovic delivered a similar pass nine minutes later, side-footing into the path of Cavani - who made no mistake when slotting into an unguarded net for his sixth goal in seven goals.
Ajax came flying out of the blocks after the interval, although the home side's defending was proving resolute.
Indeed, PSG - despite having less possession - continued to look more threatening, although Adrien Rabiot's strike over the crossbar did not trouble Cillessen.
But Ajax found a leveller midway through the second period when Ricardo Kishna's pin-point cross evaded David Luiz and found Klaassen, whose bullet diving header flew into the bottom corner.
That goal only served to restore PSG's concentration, however, with the French champions finding a clinical response.
Ibrahimovic led the way, superbly chesting down Pastore's pass before unleashing a pin-point volley into the corner.
While that goal owed much to brilliance, the hosts were gifted a third when Niki Zimling came up woefully short and allowed Cavani to round Cillessen and slot home the simplest of goals, rounding off a fine outing for Laurent Blanc's men.