Jackson and Marshall, both 21, replace regular flyhalf Jonathan Sexton and centre Gordon D'Arcy who were among four players to join Ireland's long injury list during the 12-6 defeat to England last time out.
O'Gara, Ireland's most capped player and scorer of a record 1,083 points for his country, replaced Sexton early on against England but struggled throughout and, at two weeks shy of his 36th birthday, his form has dipped markedly in the past year.
"Right up there, very difficult," the Irish coach said when asked how hard it was to leave out O'Gara, a twice Heineken Cup winner under Kidney at Munster and kicker of the drop goal that handed Ireland a first Grand Slam in 61 years in 2009.
"There's no other way of putting it but that's the best compliment I can give Paddy that he's after getting a nod ahead of Ronan."
Elsewhere Keith Earls comes off the bench to replace Munster team mate Simon Zebo on the wing while Donncha O'Callaghan will win his 93rd cap in place of Mike McCarthy at lock. Ulster's Tom Court starts at prop as Cian Healy begins a two-match ban for stamping.
Leinster wing Luke Fitzgerald, a starter for the British and Irish Lions four years ago who has been dogged by injury ever since and last played for Ireland 18 months ago, is among the replacements.
Ireland, who began the tournament without the injured trio of Paul O'Connell, Stephen Ferris and Tommy Bowe, won away to Wales in their first game of the championship.
Marshall, who drew laugher from Kidney and captain Jamie Heaslip when he said he first wathed new midfield parter Brian O'Driscoll as a nine-year-old, scored a try in a non-cap test against Fiji last November when he started alongside Jackson.
Jackson made his Ulster debut for as a teenager almost two years ago to the day and established himself in the side who reached last year's Heineken Cup final, although he was replaced early after Leinster's Sexton got the better of him.
"I forgot about rugby for a while, took a break and then just knuckled down in pre-season. The more games I've played, the more comfortable I've felt," Jackson told a news conference, referring to his performance in the 42-14 final defeat.
"I think I've come along way since the Heineken final so I don't think I'll be quite as nervous and I'm more used to dealing with my nerves now."
Prop Geoff Cross has returned to the Scotland team for the match against Ireland at Murrayfield, the only change to the side who defeated Italy earlier this month.
The Scots, who lost their opener to England, impressed in the 34-10 home victory over Italy and interim coach Scott Johnson has stuck to his guns with only Euan Murray unavailable because of his Christian faith.
On the bench, hooker Dougie Hall has recovered from a knee injury while prop Jon Welsh also wins a spot as a replacement.
"We have to improve on our last game and that's been our theme at training all week," Johnson said.
"I make no apology for saying again that we have to step up our work in the contact area. Yes, we've some talented athletes in the squad, but we have to give them the opportunities."
Scotland: 15-Stuart Hogg, 14-Sean Maitland, 13-Sean Lamont, 12-Matt Scott, 11-Tim Visser, 10-Ruaridh Jackson, 9-Greig Laidlaw, 8-Johnnie Beattie, 7-Kelly Brown, 6-Robert Harley, 5-Jim Hamilton, 4-Richie Gray, 3-Geoff Cross, 2-Ross Ford, 1-Ryan Grant
Replacements: 16-Dougie Hall, 17-Jon Welsh, 18-Moray Low, 19-Alastair Kellock, 20-David Denton, 21-Henry Pyrgos, 22-Duncan Weir, 23-Max Evans
Ireland: 15-Rob Kearney, 14-Craig Gilroy, 13-Brian O'Driscoll, 12-Luke Marshall, 11-Keith Earls, 10-Paddy Jackson, 9-Conor Murray, 8-Jamie Heaslip (captain), 7-Sean O'Brien, 6-Peter O'Mahony, 5-Donnacha Ryan, 4-Donncha O'Callaghan, 3-Mike Ross, 2-Rory Best, 1-Tom Court
Replacements: 16-Sean Cronin, 17-David Kilcoyne, 18-Declan Fitzpatrick, 19-Devon Toner, 20-Iain Henderson, 21-Eoin Reddan, 22-Ronan O'Gara, 23-Luke Fitzgerald