Debutant opener Fakhar Zaman and Sarfraz rescued their side with a 147-run partnership that gave them a respectable first-innings total of 282 before they reduced Australia to 20 for two at stumps.
The four-wicket haul, however, completed when Lyon fooled Babar Azam with his drift, dip and prodigious turn to bowl him between bat and pad, moved him to 314 test wickets, ahead of fast bowler Johnson (313).
He had started play level with Brett Lee on 310 wickets and only all-time greats Shane Warne (708), Glenn McGrath (563) and Dennis Lillee (355) are now ahead of him for Australia.
"It's a massive honour to pass the likes of Brett Lee and Mitchell Johnson," Lyon told reporters. "I have played a lot of cricket with Mitch and he has been like a big brother to me so I know there will be a banter back and forth on text message.
"I've been fortunate to play 80 test matches for Australia and be in the position to take 314 test wickets. Personally it's a great achievement and it is something I will look back on when I retire.
"I know my mum and dad are pretty proud but right now it's about doing my best and helping Australia win cricket tests."
Lyon said he felt he was bowling better than he ever had, having taken time to seek advice and work on his game, and felt he would take more wickets in the future.
"Looking back four years ago to now I've learnt a lot about my bowling," he said. "I've got more consistent and ... over the last 24 months I have improved a lot of small areas.
"I'm very confident with the way the ball is coming out of my hand ... and I've never been one for personal success or goals but ... I think I can get better."
(Reporting by Greg Stutchbury in Wellington; Editing by Toby Davis)
