England needed early wickets and Broad snared Pakistan opener Imam-ul-Haq lbw for four, but the hosts failed to make another breakthrough under the floodlights.
Hopes that a return home and a re-jigged top-order picked by new national selector Ed Smith would help rid England of the batting slumps that plagued it during a run of seven straight Tests without a victory in Australia and New Zealand quickly proved illusory as it was dismissed for just 184.
The second and final test begins Friday at Leeds, with England potentially already needing to rejig its team after rolling over meekly at the home of cricket to extend its winless run in tests to eight matches.
The third day ended with England 235-6 in their second innings - a lead of only 56 runs - and still facing the likelihood of a thumping defeat.
"It would be very easy to go into next week feeling sorry for ourselves and think there's no way forward for us -- but absolutely there is". "We have been out-performed in all three departments, we have not batted well enough, first innings in particular".
"I thought Pakistan's bowlers exploited the conditions but we played some poor shots and gave some wickets away and you can't afford to do that".
"We have to be more patient and take our opportunities when we get them".
Sarfraz also paid tribute to the influence of Pakistan coach Mickey Arthur, with the South African having launched his time in charge with a 2-2 series draw in England in 2016.
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Meanwhile the recalled Hasan, who did not play in Pakistan's win over Test debutants Ireland in Dublin concluded last week, took four for 51 in 15.2 overs.
"If you look at how the pitch performed, especially this morning, and in periods yesterday, if we get a decent score first innings it would have been very hard batting last on that surface, turning, keeping low".
"But with a five-day Test match, you've got the chance to come back and it starts tomorrow morning".
Buttler was then 66 not out and Bess 55 not out.
Alastair Cook, who top-scored with 70 in the first innings, was trapped lbw by Mohammad Abbas for one and Mark Stoneman, under severe pressure for his place in the team, made a scratchy nine before he was bowled by leg-spinner Shadab Khan before England limped to lunch at 37 for two.
Mark Wood hit one four before he nicked Mohammad Amir, bowling with the second new ball, to wicketkeeper Sarfraz Ahmed.
It was the latest memorable Lord's incident for Amir, who took six wickets in a Test innings at MCC's headquarters in 2010 - the same match where his involvement in a spot-fixing scandal led to a jail sentence and a five-year ban from cricket.
But Broad's batting has gone downhill since he was struck in the face by a bouncer from India's Varun Aaron in the fourth Test at Old Trafford four years ago.