Heads were turned before the season kicked off last week after Toronto managed to secure the services of Giovinco and Altidore from Europe.
United States international Altidore netted a brace in his first competitive outing last week as Toronto accounted for Canadian rivals Vancouver Whitecaps 3-1, while Italian recruit Giovinco - the league's highest paid player - set up the former's opener.
Toronto defender Justin Morrow was controversially sent off on the stroke of half-time after bringing down Ethan Finlay just outside the penalty area and the home team took advantage following the break with goals to Justin Meram and Kei Kamara for the Crew's first win of the campaign.
Meram headed home the opener in the 57th minute via a cross from Finlay before Kamara doubled Columbus' lead four minutes later after striking past Toronto goalkeeper Joseph Bendik.
There were goals galore at Rio Tinto Stadium in Utah as Alvaro Saborio's 86th-minute penalty earned Real Salt Lake a 3-3 draw with Philadelphia Union.
RSL trailed 2-1 at the break after a double from Fernando Aristeguieta cancelled out Javier Morales' opener.
However, Saborio spared Olave's blushes from the spot after Luke Mulholland was fouled in the area with four minutes remaining.
In other results, Chris Wondolowski's brace lifted San Jose Earthquakes past Seattle Sounders 3-2, while Octavio Rivero's 86th-minute goal gave the Whitecaps a 1-0 win at Chicago Fire.
