Martinelli, making his first Gunners start following a summer move from Brazilian club Ituano, claimed the first-half opener before completing the scoring in stoppage time.
Defender Holding, out for more than nine months with a serious knee problem, powerfully headed home the first of four goals in the final 19 minutes, with Joe Willock and Reiss Nelson also on target for the rampant hosts.
— Arsenal (@Arsenal) September 24, 2019
Arsenal were back in action little more than 48 hours since the end of Sunday's battling 10-man Premier League win over Aston Villa, with Unai Emery opting to change his entire starting XI.
On a largely positive evening for the Spanish boss, £25million summer signing Kieran Tierney impressed on his overdue debut having overcome a groin problem, while substitute Hector Bellerin joined Holding in being welcomed back from long-term injury.
However, there was also concern for Emery after young forward Emile Smith Rowe left the field on a stretcher in the first half following a clash of heads.
Forest were backed by almost 8,400 fans on their first visit to the Emirates Stadium.
After kick-off was delayed by 15 minutes due to travel issues affecting supporters, the large travelling contingent were almost silenced within 10 minutes when Nelson grazed the base of the right post from a free-kick.
The Sky Bet Championship club, who made six changes, had arrived in the capital unbeaten since the opening weekend of the campaign and having dispatched local rivals Derby in the previous round.
England Under-21 forward Nelson, searching for his maiden Gunners goal, was causing the visitors plenty of problems and played a major role in the 31st-minute opener.
The 19-year-old's clever cross-field pass was powerfully volleyed back across goal by Calum Chambers, allowing 18-year-old Martinelli to nod into the top right corner.
Arsenal were dumped out of the FA Cup when the clubs last met during the final season of Arsene Wenger's reign.
Of the players selected to start by Emery, only goal-scoring trio Holding, Nelson and Willock were involved in the 4-2 upset at the City Ground in January 2018.
Scotland international Tierney was looking to advance at every opportunity and he almost created a second for his side five minutes before the break, tricking his way past Joe Lolley and delivering an inviting cross from the left which resulted in recalled Forest goalkeeper Arijanet Muric pushing away Emile Smith Rowe's header.
In trying to score, 19-year-old Smith Rowe clashed heads with Forest captain Jack Robinson and left the pitch on a stretcher to be replaced by Bukayo Saka.
Four-time winners of this competition under Brian Clough, the away side were pinned back for much of the opening period as Gunners keeper Emiliano Martinez remained untested.
Midfielder Willock should have doubled the advantage in the 67th minute but he somehow headed wide from six yards after Saka tricked his way past Matty Cash on the left.
Forest's previous away game against the Gunners – in August 1998 – ended in a 2-1 top-flight loss at Highbury following goals from Emmanuel Petit and Marc Overmars.
Any hope of an upset was effectively ended 19 minutes from time when Holding rose unmarked to nod in a right-wing corner and claim his first goal since September 2017.
Bellerin, out since January with a knee issue, then teed up Willock for a tap-in less than a minute after replacing former Celtic man Tierney.
Nelson slotted into the top right corner following a second assist from full-back Chambers, before Martinelli completed the scoring in stoppage time with a deflected drive from distance.