When the pair reunited, the tourists still needed 33 runs to beat Australia again at the Gabba on another rain-delayed day.
But under gloomy skies, the pair managed to defeat the much-vaunted Australian attack and frustrate the home team on day four.
Deep scored the crucial points with a lead to the boundary soon after Nathan McSweeney’s outstretched hand on Australian captain Pat Cummins.
He celebrated two balls later, hitting Cummins at mid-wicket for a huge six before the umpires took them off the field for lack of light with India at 252-9, 193 runs down.
The five-match series is currently tied at 1-1. Opener KL Rahul, who top-scored with 84, said the lower-order batting showed how much fight this Indian team has. .
“Lower order scores are something we discuss in our meetings,” Rahul said.
“The bowlers also work hard on batting, so it’s good to see them get this partnership.
“Avoiding this continuation makes a huge difference.”
Lost pace leader Josh Hazlewood, who could only bowl one on Tuesday after suffering a match-ending calf injury, Cummins (4-80) and Mitchell Starc (3-83) worked hard to get wickets.
After missing much of Saturday and Monday due to rain, play was interrupted three more times on Tuesday.
During this period, India managed to get closer to the next target despite losing wickets at crucial junctures.
But Deep and Bumrah fought hard and scored 39 runs under dark skies and light rain.
“I think the only way to force the game was to impose the sequence,” Australian bowling coach Daniel Vettori said.
“There was a desperation to get the final wicket.”
Resuming the morning at 51-4, Rahul was run out from the first ball of the day when Steve Smith somehow missed a simple catch at first slip.
Rahul and India captain Rohit Sharma saw out the first half-hour and took the score to 74 before Rohit bowled a Cummins delivery that went slightly out of bounds to wicketkeeper Alex Carey.
Rahul pounced on Smith’s first ball and scored a stunning half-century with fine cover, just before rain sent the players off the field for 25 minutes.
He added 51 runs to his overnight total before Smith made amends with a stunning catch to dismiss Rahul, diving to his right and catching a hand at first slip, 20 minutes before lunch.
Nitish Kumar Reddy and Ravindra Jadeja wore 53 and looked increasingly comfortable.
But just when it looked like the duo would take the score to the necessary 246 to avoid the follow-on, Cummins stepped up as Reddy bowled for 16, leaving Jadeja with only the bowlers to try and prevent the follow-on.
Rain forced an early tea and after the break Jadeja began to take control, cultivating the strike and taking it to 77 before taking it to Mitchell Marsh with deep square leg.
Bumrah and Deep then reunited for their memorable collaboration.
