Etheridge allowed Lewis Wing's inswinging corner to drop through his hands in the 56th minute for Boro's third goal.
His rare error effectively clinched a third straight win for Neil Warnock's side and a first away victory in seven, before Wing notched a fourth eight minutes from time.
It was Middlesbrough's biggest league win in over five-and-a-half years, since they beat Ipswich at home by the same scoreline on March 14, 2015.
Blues have now lost their last three games and gone six home games without a win as they crashed to their biggest league defeat since losing 5-0 at Brentford on February 20, 2018.
But they started better and created the first chance when striker Scott Hogan headed wide from Jeremie Bela's cross.
That bright start got better and gained its reward in the 15th minute when Colin put them ahead.
The right-back crashed home a rising left-foot drive into the top corner of the net from 15 yards after Jon Toral's shot was blocked following another Bela cross.
It was Colin's first goal in 53 Sky Bet Championship appearances.
But Middlesbrough worked themselves back into the game to lead by half-time.
Midfielder Saville volleyed just wide for the visitors before Assombalonga levelled in the 27th minute with a cool, neat finish across Etheridge after Marc Bola put him through in the channel.
The striker justified his recall at the expense of Chuba Akpom to score his fourth goal of the season, ending a four-match drought on his 99th league start for the club and his 299th League appearance.
Saville put Boro ahead after 31 minutes when he side-footed home at the near post from a left-wing cross from Marvin Johnson – his seventh assist of the season.
Then came Etheridge's moment to forget, which effectively put the game beyond the home side.
But it made little difference as Middlesbrough saw out the game comfortably.
Blues' luck was summed up when defender Harlee Dean ventured forward for a shot but ballooned his effort high into the stand.
Wing scored the goal of the game when he lashed home with a low drive from 25 yards from Marcus Tavernier's pass in the 82nd minute after Assombalonga raced onto a through ball only to be held up by Marc Roberts.
Etheridge also got a firm hand on this shot, only for the ball to go underneath him and into the net.