Set a record victory target of 380 on the fifth and final day, Pakistan finished on 214 for four to leave the four-match series all square at 0-0.
Pakistan captain Inzamam-ul-Haq was 56 not out and Abdul Razzaq 25 not out when a draw was agreed with eight overs left.
Left-arm spinner Panesar took two for 60 from 27 overs.
England skipper Andrew Strauss delayed his team's declaration for over 30 minutes on Monday, but he said he was happy with the decision taken.
"Our thinking was to get Pakistan to play a game they are not accustomed to. I took some advice but it's a captain's decision," said Strauss.
"I know that the wickets here are tough to get a result on. I felt we needed to get men round the bat. We tried our hardest but we weren't able to get it done."
Inazamam, who has now made nine successive half-centuries against England, believes his team will learn a lot from playing at Lord's.
"Our team is young and a lot of them were playing at Lord's for the first time," he said.
"They were under pressure but after the first day, they played well and we want to continue that form."
Pakistan began the final session on 151 for four in their second innings, still needing a further 229 after Panesar's double strike.
Inzamam was 20 not out and Razzaq one not out at the interval, a mimimum of 32 overs left for their side to get the runs - or England the six wickets they needed - for victory.
Earlier man-of-the-match Mohammad Yousuf, whose first innings 202 was the highest individual score by a Pakistani in a Lord's Test, fell to Panesar for 48.
Panesar pitched the ball on leg-stump and spun it back to have the right-hander lbw with Pakistan now 116 for three.
Inzamam on one, then inadvertently guided Panesar past the right hand of Marcus Trescothick at first slip before almost playing on to him when 12.
Panesar though struck again when Iqbal (48) was taken in the gully by Alastair Cook.
Matthew Hoggard had dismissed both openers before lunch, Salman Butt lbw for a first-ball nought and Imran Farhat (18) taken at third slip by Paul Collingwood.
England resumed Monday on 258 for seven in their second innings, a lead of 341 which was boosted by Liam Plunkett's Test best 28.
But when he was out, Strauss declared with his side on 296 for eight.
Strauss, leading the team because of Andrew Flintoff's ankle injury, had made 128 on Sunday and so become only the third player, after Archie MacLaren in 1897/98 and Allan Lamb in 1989/90, to score a hundred in his debut Test as England captain.
His century was the fifth of the match.
In England's first innings 528 for nine declared, Collingwood struck a Test-best 186 with Cook making and Ian Bell 100 not out.
England, as well as Flintoff, were without fellow Ashes-winning bowlers Simon Jones (knee) and Ashley Giles (hip).
But Pakistan had even worse injury problems with pacemen Shoaib Akhtar (ankle), Rana Naved-ul-Hasan (groin) and Mohammad Asif (elbow), as well as batsmen Shoaib Malik (elbow) and Younis Khan (knee), all sidelined.
Ultimately, neither side had the bowling firepower to take 20 wickets on a batsman's pitch although Pakistan dropped seven catches.
England will hope to have Flintoff back in time for the second Test which gets underway at the all-rounder's Old Trafford home ground on July 27.
Flintoff though must first prove his fitness in Lancashire's County Championship match away to Kent starting Tuesday.
England 2nd Innings: (overnight: 258-7)
Fall of wickets: 1-38, 2-64, 3-141, 4-146, 5-203, 6-250, 7-253, 8-296
Did not bat: S Harmison, M Panesar
Pakistan 2nd Innings:
Fall of wickets: 1-0, 2-33, 3-116, 4-141
Did not bat: Shahid Afridi, Kamran Akmal, Mohammad Sami, Umar Gul, Danish Kaneria
Umpires: Steve Bucknor (WIS), Simon Taufel (AUS), TV umpire: Peter Hartley (ENG)
Match referee: Ranjan Madugalle (SRI)
Result: Match drawm
Series: Four-match series level at 0-0
Man-of-the-match: Mohammad Yousuf (PAK)
Jul 27-31: Second Test, Old Trafford
Aug 04-08: Third Test, Headingley
Aug 17-21: Fourth Test, The Oval