Three weeks ago both Cook and England were at a low ebb as they slumped to defeat at Lord's in the second Investec Test against India - a seventh loss in a run of 10 matches without a win.
Cook's position as captain was under heavy scrutiny, the pressure magnified by his own poor form with the bat. The situation has turned around after back-to-back victories at the Ageas Bowl and Emirates Old Trafford, with Cook scoring two good half-centuries in Southampton.
Moores had been keen to work with Cook when he took charge at the start of the summer and backed the 29-year-old to defy his critics.
Moores said: "The significant point was when he came out and said he was in it for the long haul. If people didn't want him, that was fine, he would move on - but he made pretty public his desire to captain England. He is very determined. The more people have had a go at him, the more he has said he is totally in for it.
"He is developing quickly as a captain tactically and has great values to lead with from example.
"He would admit that at times he has had a really tough ride but often that can forge somebody into something special. Hopefully for Alastair that is starting to come out a bit."
England are now heading to the Kia Oval for this week's final Test with an unassailable 2-1 lead and with spirits soaring after a win inside three days in Manchester.
India lost nine wickets after tea on Saturday to crash to defeat by an innings and 54 runs. It wrapped up a sorry match for the tourists, who had slumped to eight for four after winning the toss and then been shot out for 152 on the first day.
Even with half a day lost to rain and a sodden outfield, and a poor forecast for the final two days of the match to aid their cause, India were unable to conjure much resistance. Stuart Broad, who ended with a broken nose, took the man-of-the-match award for his first-innings six for 25, while Moeen Ali, with his rapidly improving off-spin, claimed four wickets in the last session.
Other plaudits went to Joe Root and Jos Buttler, whose seventh-wicket stand of 134 helped England to a significant first-innings lead after India's seamers had threatened to bring the match back into the balance.
Describing the last two matches, Moores said: "We have now played pretty consistently all the way through the last Test and pretty much all the way through this one. That has resulted in two wins and we have had two or three exceptional performances within that … but we have got to be pretty careful we don't get carried away. We have got a huge game at The Oval."
England have named an unchanged squad for the fifth Test with the only major issue being the fitness of Broad. His nose was fractured by an 88mph bouncer from India's Varun Aaron, and Broad went to hospital during the second innings.
The 28-year-old, who is to undergo knee surgery at the end of the series, is confident of returning to action but said on Twitter yesterday that he may need to wear protective face gear.
Broad, who attached a picture showing his bloodied and stitched nose, wrote: "Little bit sore this morning but not too bad! Doc did a great job with the stitches. On to The Oval! (With a mask)."
Steven Finn and Ben Stokes are the potential replacements in the squad should Broad not be risked.