There is no Petrov equivalent, but a drawish opening is the Slav Defense.
Best drawing weapon against 1. d4?

Why in the world would you want to draw against 1.d4??
White has permanently weakened the e3,e4 and c3 and c4 squares!

Trying for a win gives you three options: Win, lose, or draw. Trying to draw seems to take away the option for winning, then you'd only draw or lose .
Playing drawish openings is fine, but always try to play your best (for a win , if you want to improve your chess).

Why in the world would you want to draw against 1.d4??
White has permanently weakened the e3,e4 and c3 and c4 squares!
This is exactly why a4 is a much better move, it only weakens two non-central squares.

Why in the world would you want to draw against 1.d4??
White has permanently weakened the e3,e4 and c3 and c4 squares!
This is exactly why a4 is a much better move, it only weakens two non-central squares.
Right! Also the pawn advance gives the flexibility of Ra2 or Ra3 and also Ba3 or Na3
are now more viable since they do not block the a-pawn.

The stonewall through a slav move order is a good way to get a drawish game. you avoid 2.Bg5 dutch and allow your opponent to enter the exchange slav (if they wish) which you will be happy with since its mega drawish.

The question posed by the OP is mistaken. The Petrof only slightly limits the win percentage of White, though it does draw more than 2...Nc6; it mainly does so by winning fewer games.
It might be better to look for a way to wrest the initiative from White instead of trying to force a draw from the opening moves.
If one wants to strictly reduce their chances to lose against 1.d4:
The best drawing weapons are probably the Tartakower and Lasker QGDs, but to get there you have to avoid the Exchange Variation. For this I would advise a Nimzo-Indian move order (1.d4 Nf6 2.c4 e6) and on 3.Nf3 d5. If 3.Nc3 I would go into the Nimzo. You can pick something dry like the Huebner Variation against 4.e3, and there are a few approaches against 4.Qc2.
If one wants to strictly reduce their chances to lose against 1.d4:
The best drawing weapons are probably the Tartakower and Lasker QGDs, but to get there you have to avoid the Exchange Variation. For this I would advise a Nimzo-Indian move order (1.d4 Nf6 2.c4 e6) and on 3.Nf3 d5. If 3.Nc3 I would go into the Nimzo. You can pick something dry like the Huebner Variation against 4.e3, and there are a few approaches against 4.Qc2.
Relying on any QGD means you must also be prepared for a Catalan, where QID keeps you in more familiar territory.
True, you need to worry about the Catalan, but I don't think it's that bad. If one likes the QID, that does make it easier.

My personal preference is to try for the Tarrasch Defense:
Tarrasch-type positions are very active, but typically mean win or lose - either Black gets a good attack, or he loses the IQP and eventually the game.

If all you want is a draw against 1.d4, your best bet is the true orthodox QGD (i.e. Not the Tartakower, or Lasker, the true Orthodox).
BTW, the Slav is not a draw, and if White plays the exchange, Black can get active play with the 6...Bf5 or 6...a6 lines instead of 6...e6.
The Stonewall also is by no means a draw. Like the Slav, I've played this many times, and if Black plays flexibly with it, developing the Bishop via ...b6, and ...Bb7 instead of ...Bc8-d7-e8-h5, and if he follows all the specific rules in the opening (i.e. Don't play ...c6 until White has played c4, don't play the Stonewall if White can still play Bf4 and Bd3, shift gears to a classical, same with early Nh3 moves, etc.
For the person that said the Queen's Indian, you can't play that as a standalone defense. What happens after 3.Nc3 or 3.g3? In both cases, 3...b6 is just outright stupid and White gets an excellent game!
Kramposian wrote:
Is there a Petroff/Petrov equivalent against 1. d4?
Andre_Harding wrote:
Yohan_Saboba: The OP was asking about a drawing weapon...
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The best drawing weapon against 1.d4 or 1.e4 is 1....c6 (the Caro-Kann)

Best drawing weapon? Yuck. I always play to win, even against much stronger players.
Thank goodness for real chess players like Bobby Fischer, who even with the black pieces, and even against the strongest grandmasters, he would always play to win.
& Magnus. Maybe that's why they are the best.
Is there a Petroff/Petrov equivalent against 1. d4?