Lambert, who's thumping header at Wembley in midweek finally killed off Scotland 3-2 in a fiery friendly, had been held at bay by a resolute West Bromwich Albion defence at The Hawthorns.
However, the striker made no mistake from the penalty spot in the dying seconds to snatch a 1-0 victory for the visitors.
"It's a great way to finish the week. It'll be a week that I'll never forget in my life and to finish it off with a win for Saints is superb," said 31-year-old Lambert.
"I wanted to carry it on into this game by getting on the scoresheet from open play, but I found it hard against the centre back pairing that West Brom played as I think they're very good and it was hard again today.
"Fair play to the defence because I thought defensively we stood up and they were warriors today, so full credit to them."
Saints fullback Luke Shaw won the penalty when he was brought down by Youssouf Mulumbu after a darting run and Lambert made no mistake thumping the spot-kick past keeper Ben Foster.
"I didn't get much joy against them all afternoon, but Luke's done a little bit of magic there at the end to create the winning goal," Lambert told Saints TV.
"They were just starting to get back into it before we scored the goal, but Luke has done so well.
"I tried to just whack it into that corner and thankfully, it's gone right into the corner because I think he's got fingertips to it as well.
"I knew I'd caught it sweet because it would have been a hell of a save, if he'd saved it," Lambert said of fellow England international Foster's attempt to keep the ball out.
The win left Southampton sixth in the standings and the three points drew a reminder that it took five games to achieve the same feat last year.
Lambert hopes to use the victory in the Midlands as a springboard to greater success.
"I can't overestimate how important it is to get the first points on the board," he said. "It gives you confidence to go on into the season and to get it away from home is superb."
Saints boss Mauricio Pochettino added: "I think in the overall reading of the game, we were superior to West Brom.
"You always have to believe you are going to win, through to the last whistle, and because of that I want to congratulate my team," he told the BBC.
"Even in the second half, when West Brom were pressing us quite hard, my team showed the resolve to keep it at 0-0 and we were able to get that winning goal in the end."