I don't even think the parents "need" to be highly educated themselves. It's often enough that they value education and make sure their kids take it seriously, do their homework, read for pleasure, do revision, etc., right from the earliest age, as well as making sure they can read and write basic stuff before they start school. Give them the tools and encouragement to want to learn and put them in the right place to learn.
My mother was a teacher, but she didn't show any interest at all in my education at secondary school. Never once attended a parent's evening, never bothered asking for my termly reports, etc. I was horrendously bullied and she just basically shrugged and told me to toughen up. No pressure at all for me to do homework nor revise. Never asked how my day had been. If I wanted some extra resources for homework or a project, I was left to fend for myself, she wouldn't buy any books, wouldn't take me to the library, etc. She had a lot going on in her life, and somehow thought that because she'd gone to a good school and got a good education, then I'd be OK at the secondary school (a crap comp) as she just didn't realise how bad a crap comp can be. It was only in much later years when we could have adult conversations about it that it finally dawned on her that she was part of the problem why I left at 16 with no qualifications at all!
Me and OH were both on the same page with our son. Neither of us had gone to uni, both had suffered crap comps. Both had pulled ourselves up by doing evening classes to get qualifications, etc. - i.e. the hard way by studying alongside full time crap jobs!
We made sure our son could read and write and knew his numbers and basic sums before he started primary school. Our "plan" was to ensure he never fell behind and to keep him just ahead of the curve. We weren't teachers, but we researched the kind of things they were taught in school each year group and did "fun" learning alongside. We were well on top of his school work, we attended every parents evening, every school event, looked at his school books whenever he brought anything home.
We spent a lot of time with him helping him choose a secondary school. Went to every open day in the area, learned lots of information by attending their intro talks, talking to teachers during tours, etc. He chose the school most suited to him which was probably the most difficult to get to, but we facilitated the transport to get him there.
Throughout secondary, we were heavily involved. Checked his homework diary every day (then the online version later), always looked at his exercise books when he came home to check what marks he'd been given, talked through any areas where he seemed to struggle, etc. We could keep up, between us, until GCSEs, but by then he'd got into good habits, revision, homework, paying attention in class, so we had to take a step back and leave him to it as we really couldn't help at GCSE level. He passed them all - all 8s and 9s! Went into sixth form - again, far beyond what we could help with, but again, he was on the crest of the wave so as long as he kept up, did what the teachers asked of him, he was fine and ended up with a string of A*s.
Neither of us had been to Uni, but we'd basically "primed" him to go from an early age, so it was just the next stage for him. We had noone in the family to ask advice, so between the three of us did lots of googling for uni websites and we also learned a lot from fora like MN! Travelled all over the country to go to open days, then offer holder days, etc. He got in his first choice uni, and got a First degree in Maths. Our work was done!
So, no, you don't really need parents who've had a top class education themselves, expecially now so much information is available on the internet. It's attitude that matters most. One of my son's life long friends is from a nearby council estate with a lorry driving father and a shop working mother - again, no real education behind them, and certainly no professions, but they had the same kind of "highly motivated" parentage and he likewise did exceptionally well at school, then Uni (again, first in family) and is currently working as a programmer in Silicon Valley!
Personally, I don't really think that an academic background necessarily means the children are going to outperform. These days, I think parental attitude and involvement is more important. Of course, best case scenario is to have academic parents AND highly motivated/invested parents!