Leeds showed signs of a return to their fine form from earlier in the season at Tranmere but now face games against Southampton on Saturday, a visit from Millwall on March 22, and then head to League One leaders Norwich City on March 27.
Those three matches could have a huge bearing on who goes up from League One and Bates knows it is going to be a nerve-jangling few weeks for manager Simon Grayson and all at Elland Road.
"Simon had said to me well before Tuesday night that we've just got to keep calm and hold our nerve, and he was right," the chairman told Yorkshire Radio.
"Tuesday's win puts us five points clear and improves our goal difference which is worth another point.
"Brighton did us a favour on Monday when they got a result at Colchester, Swindon seem to be struggling a bit, Huddersfield have had a couple of bad results, and we should be looking forward to our remaining games with confidence.
"Every other club will have the same jitters at this stage of the season, but as Simon has always said, we're all in this together at Leeds and we will try to do it all together.
"The next few games will go some way to deciding both our fate and that of the three teams we play," said the chairman.
"We're as good as anybody, if not the best, but it takes two to tango. We've beaten Norwich and Southampton this season, but Millwall beat us there and Swindon, who still have to come here, also beat us, so we owe them one!"
Manager Grayson was also delighted to see his side get back to something like their best form at Prenton Park.
"We were composed on the ball. It's what we needed and what's been coming.
"You could sense over the past week we've been getting back to that. You can't get too carried away, we have another 11 games to go, but if we can replicate that performance we will be a handful for everyone.
"Now our focus turns to the weekend. We have three big games coming up and we know we can win them."
Southampton 13/8, Leeds 13/8, Draw 12/5