Godden strike sees Coventry share points with LutonMatt Godden's first goal since August earned 10-man Coventry a point and halted Luton's winning run.
The Hatters went ahead inside the opening minute when defender Tom Lockyer tapped home.
But Godden equalised with a penalty after Viktor Gyokeres was brought down by Gabriel Osho just before half-time.
Both sides had chances to win it after the break, with Sky Blues midfielder Josh Wilson-Esbrand red-carded late on for a foul on Fred Onyedinma.
Coventry were forced to reshuffle their line-up just before kick-off, when midfielder Ben Sheaf suffered a calf injury in the warm-up, with Kasey Palmer given a starting role in his place.
The late change may have contributed to a disorganised start which saw Luton take the lead after only 40 seconds with Alfie Doughty wriggling free on the right to deliver a cross that was only half-cleared, allowing Lockyer to steer home from close-range.
However, it was the Sky Blues who created the better opportunities during the remainder of the first period, with their top scorer Gyokeres forcing a fingertip save from Luton goalkeeper Ethan Horvath, while Palmer manufactured a chance for himself, only to fire off-target.
But Coventry levelled just before the interval through Godden's spot-kick after referee Steve Martin ruled that Osho had fouled Gyokeres.
Palmer almost put his side ahead soon after the restart with an attempt that looped over Horvath but struck the crossbar.
The Luton goalkeeper also denied Gyokeres and Luke McNally, while the visitors - who had won six of their last seven games - almost snatched a winner through substitute Cauley Woodrow, but he was foiled by an impressive double save from Ben Wilson.
Coventry finished the game with 10 men after Wilson-Esbrand, on loan from Manchester City, was dismissed five minutes from time.
The draw means both sides' league positions remain unchanged, with Luton fourth and Coventry 15th.
Coventry manager Mark Robins told BBC Coventry & Warwickshire:
"It was a really hard-fought point, but nothing short of what we deserved. I thought we were pretty good after the start we had.
"We lost Ben Sheaf in the warm-up and that really hurt us. Having to make a lot of adjustments minutes before we got out really contributed to the first goal because we looked a bit messed-up.
"The goal was poor but the good thing about it was the character they showed to get back in it - that was really important.
"We've not caved and we got a bit of confidence in the second half. We've looked dangerous and looked like we could hurt them."