Younis made a brilliant 173 and shared a record stand of 363 with Mohammad Yousuf (192), Pakistan's best for any wicket against England, as the tourists fought back on Sunday.
But, in sight of a double century, 28-year-old vice-captain Younis joined the long list of batsmen run out by the less-than-rapid Inzamam.
His skipper played the ball onto the onside for what was always a tight single and Younis failed to beat Sajid Mahmood's direct hit from mid-wicket.
Younis's departure sparked a mini-collapse that saw four wickets lost for three runs in 10 balls shortly before tea.
"It's not the first time I've been run out. In the last series against India, I was run out for 199 with Shahid Afridi," Younis said with a smile.
Inzamam himself exited in comical style soon afterwards when, having swept left-arm spinner Monty Panesar, he overbalanced and fell into his own stumps to be out hit wicket.
"No I didn't laugh," said a beaming Younis. "He's our captain."
Pakistan made 538, a lead of 23, before England ended the day on three without loss in their second innings.
Batsmen on both sides have dominated this match so far but Younis said Pakistan, 1-0 down in the four-match series, had a chance of winning despite a seemingly placid pitch.
"The pitch looks like a batting pitch but if, you bowl well, things can happen as there are some cracks."
Younis, reflecting on his first Test hundred against England, said: "I wanted to lead by example, play my shots and encourage our youngsters."
And he insisted there was no mystery to his huge stand with Yousuf. "The key is that all the time we took quick singles."
Someone else celebrating a 'first' was England all-rounder Paul Collingwood who, in his 64th over of trying, finally took a Test wicket when Faisal Iqbal fell lbw to the Durham medium-pacer for a first-ball nought.
"I've been toiling away for some time, so my strike-rate needs to come down a touch," joked the 30-year-old Collingwood, now in his 14th Test.
"I was running out of breath actually. I didn't think he (West Indian umpire Billy Doctrove) was going to give it."
Collingwood added England were comfortable with their position.
"They (Younis and Yousuf) put a great partnership on, it was as simple as that.
"We didn't think the game was running away from us. We just knew we had to keep going and, once we got the breakthrough, put pressure on the new batsman.
"Thankfully, we got that run out and we had a crazy five minutes."
However, Collingwood said there was plenty of time for further twists and turns. "There's a long way to go, in two days a lot can happen.
"We've now got to go out there and play as if it's the first innings and then we can re-assess as the day (Monday) goes on."