Skipper Steven Gerrard was sent off two minutes from time as Lampard's 86th-minute penalty earned the Three Lions a vital point in their quest to reach Brazil 2014.
The hosts were saved when Yevhen Khacherdi blocked Danny Welbeck's flick with his arm, allowing Lampard to make no mistake from the spot.
Gerrard's dismissal followed shortly afterwards for a second yellow card.
The Liverpool man becomes the 14th England player to be sent off, although the damage is not too bad as he only misses the visit of San Marino next month.
Ukraine will be cursing a missed opportunity, though.
Already nursing a sense of grievance after having a perfectly good goal ruled out when the two sides met at Euro 2012, Oleg Blokhin's men came agonisingly close to what would have been a deserved victory.
In Yevgen Konoplianka, they had not only the game's star performer but also scorer of a goal worthy of winning any match.
And, while defeat was avoided, clearly there is so much work ahead of Hodgson and his team if they are to reach Brazil 2014.
It had not gone unnoticed that the last time England went into a competitive game with John Terry, Ashley Cole and Rio Ferdinand all missing from their starting line-up was against Croatia almost five years ago.
That miserable night was the last time England had lost a qualifying match on home soil.
It was a record that soon became obvious was going to be tested.
Only three minutes had elapsed when Oleg Gusev's cross flicked off Leighton Baines, dipped over Joe Hart and clipped the outside of a post.
Joleon Lescott cleared another Gusev cross, then Roman Zozulya failed to capitalise on Konoplianka's neat approach work.
During those dodgy opening minutes, England's passing was awful, costing them a chance to build up any momentum.
Five-goal winners in Moldova on Friday, third-ranked team in the world, any sense of superiority was shaken out of England by spirited opponents.
Andriy Shevchenko's retirement, far from weakening the team, created a greater bond, which new skipper Anatoliy Tymoschuk marshalled around the field in impressive fashion.
It might have been different had Jermain Defoe's thunderous effort not been ruled out.
Defoe's disbelief was obvious. Yet it was also beyond doubt he had shoved a textbook rugby hand-off into the neck of Andriy Yarmolenko, who made the most of it.
Gerrard was trying to inspire, like a good captain should.
Clearing a goalbound Ruslan Rotan effort at one end, driving a pass through for Defoe at the other, the striker's flick almost releasing James Milner.
It was the prelude to Cleverley's succession of glaring misses.
Defoe showed admirable unselfishness when he opted to steer Gerrard's cross back into the six-yard box rather than go for goal himself from an acute angle.
Cleverley raced in, looking certain to gobble up the chance with only Andrei Pyatov to beat.
Unfortunately, the Manchester United man fired straight at the Ukraine goalkeeper, whose reactions were up to the task.
Cleverley then flicked Lampard's pass well wide from a good position, before, as if underlining the folly of Hodgson's comparison with Cesc Fabregas, lifting the ball against the outside of a post from Milner's pass.
Amid the personal anguish, Ukraine had seized the initiative.
After Denys Garmash had let England off the hook by heading over when he crept into space to meet Yevgen Selin's cross, Konoplianka showed them no mercy.
Stepping inside Gerrard, the highly-rated midfielder sent a 25-yard effort curling over Hart and into the top corner.
In a second-half littered with yellow cards - six of them for England including Gerrard's double caution - Leighton Baines needed to make a timely intervention to prevent Zozulya reaching Konoplianka's cross.
Glen Johnson, among those to get booked after the break, went close at the other end but the introductions of Danny Welbeck and Daniel Sturridge were inevitable given how the game was panning out.
The decision to replace Baines with Ryan Bertrand was less obvious, especially as young duo Raheem Sterling and Adam Lallana both offered more attacking invention from the bench for all their inexperience.
Welbeck almost profited from Sturridge's cross nine minutes from time, but prodded against a post.
Redemption came shortly afterwards, with Lampard converting from the spot, just as he did in Chisinau on Friday.
But the outcome will fool no one, least of all Hodgson, into thinking that England really do deserve to be rated as highly as FIFA suggest.