Gerrard has been critical of his side in recent weeks as they have fallen 12 points behind Celtic at the top of the Scottish Premiership.
But the former Liverpool captain was bursting with pride as Ryan Kent scored the only goal just after the hour mark in northern Portugal and the visitors should have scored many more.
"Super proud of the players. To a man tonight they were outstanding. I thought they were faultless, certainly out of possession," said Gerrard.
"This is no fluke. This has come from sheer hard graft."
Rangers were without top scorer Alfredo Morelos through suspension and the absence of the Colombian could have proved costly as they missed a host of big chances before the break.
Morelos's replacement Florian Kamberi fired too close to Matheus in the Braga goal before Ianis Hagi dragged another huge opportunity wide.
Hagi, son of Romanian legend Gheorghe Hagi, scored twice to turn the tie around at Ibrox in the first leg but missed the chance to give Rangers breathing space from the penalty spot just before half-time.
Raul Silva was penalised for handling a corner inside his own box, but Matheus made a brilliant save to turn Hagi's penalty behind.
Kent has been criticised for his lack of impact when Rangers have most needed their £7 million signing most of late.
However, the former Liverpool winger produced a big goal when he had too much pace for the Braga defence to latch onto a long ball before firing low into the far corner.
Gerrard was scathing of his side's defending in a 2-2 draw at St Johnstone on Sunday, but the visitors stood up to deny a Braga team that are unbeaten in their last 11 domestic games.
Rangers' first win in a European knockout tie for nine years means they will be in the hat for the last-16 draw on Friday.
"We knew there was an opportunity," added Gerrard. "We need to enjoy tonight. We'll be really proud when the draw is made."
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