Ferrer had no trouble accounting for Japan's Kei Nishikori winning 6-2, 6-1, 6-4 and then the 10th seed Almagro was helped by the eighth-seeded Serbian Janko Tipsarevic retiring injured when the Spaniard was leading 6-2, 5-1.
Ferrer, who will finish the Australian Open as the world No. 4 no matter what, took advantage of a 16th seed from Japan who was far from his best.
Surprisingly Ferrer had never beaten Nishikori, but he empathically turned that around dropping just seven games in three sets to advance to his fifth straight Grand Slam quarter-final.
Ferrer has long threatened to be a Grand Slam contender, but Novak Djokovic, Roger Federer, Rafael Nadal and Andy Murray have continually got in his way. Nadal is not in Melbourne this year and Ferrer looks to have his best chance taking it up to the other three when it matters.
The 30-year-old Spaniard will next face his compatriot Almagro, who got a virtual free pass into the quarter finals with his opponent Tipsarevic forced to withdraw with a foot injury.
Almagro, the 10th seed, was already well on top leading 6-2, 5-1 but then the Serbian felt some sharp pain in his foot and could not take any further part in the patch.
The 28-year-old was devastated to have to retire hurt in the fourth round and is still unsure exactly what the problem is.
"I was not able to stand on my left foot. I haven’t seen the doctor yet, I just did a urine and blood test, and I don’t know what they will show," Tipsarevic said.
"It happened when I was 4-2 down in the second set and I feel horrible. Nico was leading and he was playing great tennis, I don’t think I played badly in the beginning, he was just hitting with an enormous amount of firepower from both wings, but I was feeling great today.
"In yesterday during warm up I wasn’t tired at all from my previous matches and it was a beautiful day for tennis, and I really felt I could play good, and I cannot be more pissed off with the way that I finished off."
Meanwhile, Czech Berdych is also into the quarter finals comfortably accounting for big-serving South African Kevin Anderson, 6-3, 6-2, 7-6.
The fifth-seeded Czech cruised through the first two sets dropping just five games along the way, but Anderson has had a good summer in Australia at the Hopman Cup in Perth and by making the final of the Sydney International.
He wasn’t about to lie down and the third set went all the way to a tie-break where it was a marathon affair with Berdych eventually prevailing 15 points to 13.
Berdych was happy to come through Anderson in straight-sets and will now take on the winner of the fourth round clash between world No. 1 Djokovic and Swiss 15th seed Stanislas Wawrinka in his third straight Australian Open quarter-final.
"I had my chances through all the third set and I should have taken it before the tie-break, but I'm just happy to make it through now," Berdych said.
"I have played three sets in all my matches so far so I have been able to save some energy, which is always helpful in a long tournament like this. This is my third quarter-final and hopefully it's third time lucky.
"Novak is a champion and is a great player, but this is my third quarter-final in-a-row here and I don’t want to end up in the same place as the last two years. I will try my best and try as hard as possible to get through to the next round."