Wales sit fifth in the table after falling to a third defeat in four outings following a 13-9 loss to France last Saturday, with its only win coming against Scotland on 13 February.
However, Pivac's team will be boosted by the return of Jones, who comes back into the starting side for the first time since suffering a shoulder injury against New Zealand at the end of October.
Biggar retains the captaincy despite 36-year-old Jones returning, with the former set to become the seventh Welshman to win 100 caps for his country.
Coach Pivac, who has made seven changes to his team that lost against table-toppers France, believes the pair deserve to share their milestone appearances together.
"We've said with other players reaching 100 appearances what an achievement that is and for Dan I know he's been looking forward to this moment for a long time," Pivac told reporters on Tuesday.
"For him to achieve it with Al, who is also getting the milestone of 150 caps – which no other player has ever done – I think it's fitting for those two to share the day.
"They've played a lot of rugby together and have a healthy respect for each other. They've given so much for the game in Wales."
Gareth Davies is in line for his first start in this year's Six Nations, with Johnny McNicholl, Louis Rees-Zammit and Willis Halaholo all recalled in the backline as well.
Meanwhile, Dewi Lake, Dillon Lewis and last year's Lions captain Jones are the forwards who come in, with Ryan Elias, Alex Cuthbert, Jonathan Davies, Tomas Francis, Liam Williams, Tomos Williams and Will Rowlands dropping out of the starting side.
On the changes, Pivac added: "We've made a few changes this week. With one game to go there are some players we need to see out there and put them in the matchday 23.
"We've certainly selected a side which we think can get the job done. Clearly that's what we're here for. There's an opportunity to move up that table, so we think this is an exciting team and one we're looking forward to seeing out there.
"Italy are a side that's improving, they've had some bad luck here and there and with a new coach transitioning we know it takes a bit of time.
"But we know they've got some very good rugby players and as you saw against Scotland they troubled them in that second half and for long periods of the first. So we're going to have to be on our game and we're very much looking forward to playing at home again this weekend.
"We had a good result against Scotland, gave the fans something to cheer about and came very close against an in-form France. Obviously disappointed we couldn't get across the line for our fans there and we hope we can do that this weekend and finish on a high."
Wales team: Johnny McNicholl, Louis Rees-Zammit, Owen Watkin, Uilisi Halaholo, Josh Adams, Dan Biggar, Gareth Davies; Gareth Thomas, Dewi Lake, Dillon Lewis, Adam Beard, Alun Wyn Jones, Seb Davies, Josh Navidi, Taulupe Faletau.
Replacements: Bradley Roberts, Wyn Jones, Leon Brown, Will Rowlands, Ross Moriarty, Kieran Hardy, Callum Sheedy, Nick Tompkins.