Munich had their eight-match winning streak ended by a 2-1 defeat to Leverkusen at their Allianz Arena last Sunday, but Schweinsteiger said his side had proved themselves after that loss.
The Bavarians trounced Hamburg in a 3-0 win as they opened a seven-point lead at the top of the table. Schweinsteiger was joined on the scoresheet by Thomas Mueller and Toni Kroos in Hamburg on Saturday in an impressive second-half display.
"It was important to provide some answers [after the Leverkusen match], and we've not won that often in Hamburg recently. We were determined to do it today," said Schweinsteiger who scored Bayern's first.
With second-placed Schalke 04 suffering a shock 3-2 defeat at Hoffenheim, results this weekend helped Bayern, as both third-placed Eintracht Frankfurt and Borussia Dortmund drew.
"It's been a very good round of matches for us. Naturally, we knew the other scores before kick-off and we were even more motivated," added Schweinsteiger.
Bayern coach Jupp Heynckes was delighted with his team's performance and praised his foreign imports, including France's Franck Ribery and Croatia's Mario Mandzukic.
"I'm delighted with the team's approach," said Heynckes with Bayern hosting Lille in the Champions League on Wednesday.
"The way we chalked up the victory was first class, it was outstanding. "That's shown by the team spirit in this group. For example, Franck was exceptional today, but Mario was just as important, for his work-rate, pressing and defending.
"That's the hallmark of my team at the moment: everyone's looking out for everyone else, we're going for success as a unit."
After his side's impressive recent form with four wins in six games, Hamburg had suffered a rude awakening.
"We were OK in the first half, we had a couple of chances on the break, and we kept it tight - until just before half-time," said Hamburg coach Thorsten Fink.
"We fell apart after the opening goal. Bayern were simply too good and we weren't at our best. "We showed too much respect, we didn't play to the best of our ability, and Bayern were obviously outstanding."
With Germany goalkeeper Manuel Neuer in the Bayern goal, Hamburg goalkeeper Rene Adler has put himself back in contention for the national team, but the 27-year-old admitted his team were outplayed.
"Bayern were in a different league, too good for us," said Adler. "We didn't play well, partly because they were so good. 'It wasn't much of a day for us. We could have done without the second half."
Hamburg's Dutch midfielder Rafael van der Vaart said Bayern had proved their place as league leaders.
"Bayern are the best team in the league and deserved to win," he said. "We were only on the pitch for the first 15 minutes. "We didn't stand a chance after that. There's no shame losing to Bayern, but we need a result next week."